problem solving practice slope answer key

Slope calculator MCQs

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Slope Worksheets

The slope (or gradient) of a line is a number that denotes the 'steepness' of the line, also commonly called 'rise over run'. Knowledge of relevant formulae is a must for students of grade 6 through high school to solve some of these pdf worksheets. This page consists of printable exercises like introduction to slopes such as identifying the type and counting the rise and run; finding the slope using ratio method, slope-intercept formula and two-point formula; drawing lines through coordinates and much more! Employ our free worksheets to sample our work. Answer keys are included.

Printing Help - Please do not print slope worksheets directly from the browser. Kindly download them and print.

Identify the Types of Slopes

Introduction to slopes: Based on the position of the line on the graph, identify the type of slope - positive, negative, zero or undefined. This exercise is recommended for 6th grade and 7th grade children.

Download the set

Draw Lines on a Graph: Types of Slopes

The first part of worksheets require students to plot the points on the graph, draw the line and identify the type of slope. In the next section, draw a line through the single-point plotted on the graph to represent the type of slope mentioned.

Count the Rise and Run

Based on the two points plotted on a graph, calculate the rise and run to find the slope of the line in the first level of worksheets. Find the rise and run between any two x- and y- coordinates on the line provided in the second level of worksheets. This practice resource is ideal for 7th grade and 8th grade students.

Graph the Line

Draw a line through a point plotted on the graph based on the slope provided in this set of pdf worksheets which is suitable for 9th grade children.

Fun Activity: Slope of the Roof

This set of fun activitiy worksheets contains houses with roofs of various sizes. Find the slope of the roof of each house. Answers must be in the form of positive slopes.

Find the Slope: Ratio Method

Use the x- and y- coordinates provided to find the slope (rise and run) of a line using the ratio method. A worked out example along with the formula is displayed at the top of each worksheet for easy reference.

Find the Slope: Line segments in a Triangle

Triangles are represented on each graph in this assembly of printable 8th grade worksheets. Learners will need to identify the rise and run for each of the three line segments that are joined to form a triangle.

Two-Point Formula

Employ the two-point formula that is featured atop every worksheet along with a worked out example. Substitute each pair of x- and y- coordinates in the given formula to find the slope of a line.

Plot the Points and Find the Slope

Plot the points on the graph based on the x- and y-coordinates provided. Then, find the slope of each line, so derived. Some problems contain x- and y-intercepts as well.

Find the Missing Coordinates

In this series of high school pdf worksheets, the slope and the co-ordinates are provided. Use the slope formula to find the missing coordinate.

Slope-Intercept Form

This set of printable worksheets features linear equations. Students are required to find the slopes by writing linear equations in slope-intercept form.

Related Worksheets

» Point-Slope Form

» Slope-Intercept Form

» Two-Point Form

» Equation of a Line

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Key to Algebra Workbooks

Key to Algebra offers a unique, proven way to introduce algebra to your students. New concepts are explained in simple language, and examples are easy to follow. Word problems relate algebra to familiar situations, helping students to understand abstract concepts. Students develop understanding by solving equations and inequalities intuitively before formal solutions are introduced. Students begin their study of algebra in Books 1-4 using only integers. Books 5-7 introduce rational numbers and expressions. Books 8-10 extend coverage to the real number system.

Calculate the Slope of a Line – Practice Questions

problem solving practice slope answer key

Posted by Brian Stocker
Date February 25, 2019
Comments 3 comments

Finding the Slope of a Line

The slope of a line is the direction and the steepness of the line. Slope is usually the letter m ;

Slope is calculated by finding the ratio of the “vertical change” to the “horizontal change” between two points on a line. Sometimes the ratio is expressed as a quotient (“rise over run”), giving the same number for every two points on the line. A line that is decreasing has a negative “rise” and a negative slope.

If a line is horizontal the slope is zero .

$m<0$

If a line is vertical the slope is undefined

The rise of a line, between two points, is the difference between the height at those two points, y 1 and y 2 , so the equation is ( y 2 − y 1 ) = Δ y . In basic geometry, we examine short distances, otherwise we would have to incorporate the curvature of the earth. The run, is the difference in distance from a fixed point along a horizontal line, or ( x 2 − x 1 ) = Δ x .

The equation to calculate the slope of a line, m, is:

Calculate the Slopr of a Line - Practice Questions

1. What is the correct order of respective slopes for the lines above?

a. Positive, undefined, negative, positive b. Negative, zero, undefined, positive c. Undefined, zero, positive, negative d. Zero, positive undefined, negative

2. Find the slope of the line above.

a. 5/4 b. -4/5 c. -5/4 d. -4/5

3. What is the slope of the line above?

a. 1 b. 2 c. 3 d. -2

4. What is the slope of the line above?

a. -8/9 b. 9/8 c. -9/8 d. 8/9

5. With the data given above, what is the value of y1?

a. 0 b. -7 c. 7 d. 8

4. A (x1, y1) = (-9, 6) & (x2, y2) = (18, -18) Slope=(-18 – 6) / [18 – (-9)] = -24/27= -(8/9)

Most Common Geometry Mistakes on a Test

Not clearly labeling or identifying the given and unknown information in a problem
Not understanding the properties and definitions of basic geometric figures (e.g. line, angle, triangle, etc.)
Incorrectly using basic formulas (e.g. area of a triangle, Pythagorean theorem)
Incorrectly interpreting geometric diagrams
Not understanding the relationship between parallel lines and transversals
Not understanding the relationship between angles and their degree measures
Not understanding the relationship between perimeter and area

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How to Solve Linear Inequalities – Quick Review and Practice

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Slope Formula Worksheets

Related Topics: More Math Worksheets More Printable Math Worksheets 7th Grade Math

There are six sets of coordinate geometry worksheets:

Midpoint Formula
Distance Formula

Slope Formula

Standard Form & Slope-Intercept Form
Parallel Lines
Perpendicular Lines

Examples, solutions, videos, and worksheets to help grade 7 students learn how to use the slope formula to find the slope of a line passing through two points on the coordinate plane.

How to use the Slope Formula to find the slope of a line passing through two points?

The slope formula is used to calculate the slope of a line that passes through two points in a two-dimensional Cartesian coordinate system (x, y). The slope (m) represents the rate at which the line rises or falls as you move from left to right. The formula for calculating the slope between two points (x 1 , y 1 ) and (x 2 , y 2 ) is as follows:

m = (y 2 - y 1 ) / (x 2 - x 1 )

In this formula:

(x 1 , y 1 ) are the coordinates of the first point on the line.
(x 2 , y 2 ) are the coordinates of the second point on the line.
m is the slope of the line that passes through these two points.

To calculate the slope between two points, you subtract the y-coordinates (vertical change) and divide it by the difference of the x-coordinates (horizontal change) between the two points.

Example: Use the slope formula to find the slope of the line passing through these two points A(3, 4) and B(6, 8). m = (8 - 4) / (6 - 3) m = 4 / 3

So, the slope of the line passing through points A and B is 4/3.

Click on the following worksheet to get a printable pdf document. Scroll down the page for more Slope Formula Worksheets .

More Slope Formula Worksheets

Printable (Answers on the second page.) Slope Formula Worksheet #1

Online Quadrants of Coordinates Slope of a Line Slope and Intercept of a Line Midpoint Formula 1 Midpoint Formula 2 Distance Formula 1 Distance Formula 2

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Slope Intercept Form Worksheets

The worksheets given here need students to have sound knowledge of the slope-intercept form of an equation as they got to work with the y-intercepts and slopes while solving the questions.

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A: ( 5 , 1 ) ( 5 , 1 ) B: ( −2 , 4 ) ( −2 , 4 ) C: ( −5 , −1 ) ( −5 , −1 ) D: ( 3 , −2 ) ( 3 , −2 ) E: ( 0 , −5 ) ( 0 , −5 ) F: ( 4 , 0 ) ( 4 , 0 )

A: ( 4 , 2 ) ( 4 , 2 ) B: ( −2 , 3 ) ( −2 , 3 ) C: ( −4 , −4 ) ( −4 , −4 ) D: ( 3 , −5 ) ( 3 , −5 ) E: ( −3 , 0 ) ( −3 , 0 ) F: ( 0 , 2 ) ( 0 , 2 )

Answers will vary.

ⓐ yes, yes ⓑ yes, yes

ⓐ no, no ⓑ yes, yes

x - intercept: ( 2 , 0 ) ( 2 , 0 ) ; y - intercept: ( 0 , −2 ) ( 0 , −2 )

x - intercept: ( 3 , 0 ) ( 3 , 0 ) , y - intercept: ( 0 , 2 ) ( 0 , 2 )

x - intercept: ( 4 , 0 ) ( 4 , 0 ) , y - intercept: ( 0 , 12 ) ( 0 , 12 )

x - intercept: ( 8 , 0 ) ( 8 , 0 ) , y - intercept: ( 0 , 2 ) ( 0 , 2 )

x - intercept: ( 4 , 0 ) ( 4 , 0 ) , y - intercept: ( 0 , −3 ) ( 0 , −3 )

x - intercept: ( 4 , 0 ) ( 4 , 0 ) , y - intercept: ( 0 , −2 ) ( 0 , −2 )

− 2 3 − 2 3

− 4 3 − 4 3

− 3 5 − 3 5

− 1 36 − 1 36

− 1 48 − 1 48

slope m = 2 3 m = 2 3 and y -intercept ( 0 , −1 ) ( 0 , −1 )

slope m = 1 2 m = 1 2 and y -intercept ( 0 , 3 ) ( 0 , 3 )

2 5 ; ( 0 , −1 ) 2 5 ; ( 0 , −1 )

− 4 3 ; ( 0 , 1 ) − 4 3 ; ( 0 , 1 )

− 1 4 ; ( 0 , 2 ) − 1 4 ; ( 0 , 2 )

− 3 2 ; ( 0 , 6 ) − 3 2 ; ( 0 , 6 )

ⓐ intercepts ⓑ horizontal line ⓒ slope–intercept ⓓ vertical line

ⓐ vertical line ⓑ slope–intercept ⓒ horizontal line ⓓ intercepts

ⓐ 50 inches
ⓑ 66 inches
ⓒ The slope, 2, means that the height, h , increases by 2 inches when the shoe size, s , increases by 1. The h -intercept means that when the shoe size is 0, the height is 50 inches.
ⓐ 40 degrees
ⓑ 65 degrees
ⓒ The slope, 1 4 1 4 , means that the temperature Fahrenheit ( F ) increases 1 degree when the number of chirps, n , increases by 4. The T -intercept means that when the number of chirps is 0, the temperature is 40 ° 40 ° .
ⓒ The slope, 0.5, means that the weekly cost, C , increases by $0.50 when the number of miles driven, n, increases by 1. The C -intercept means that when the number of miles driven is 0, the weekly cost is $60
ⓒ The slope, 1.8, means that the weekly cost, C, increases by $1.80 when the number of invitations, n , increases by 1.80. The C -intercept means that when the number of invitations is 0, the weekly cost is $35.;

not parallel; same line

perpendicular

not perpendicular

y = 2 5 x + 4 y = 2 5 x + 4

y = − x − 3 y = − x − 3

y = 3 5 x + 1 y = 3 5 x + 1

y = 4 3 x − 5 y = 4 3 x − 5

y = 5 6 x − 2 y = 5 6 x − 2

y = 2 3 x − 4 y = 2 3 x − 4

y = − 2 5 x − 1 y = − 2 5 x − 1

y = − 3 4 x − 4 y = − 3 4 x − 4

y = 8 y = 8

y = 4 y = 4

y = 5 2 x − 13 2 y = 5 2 x − 13 2

y = − 2 5 x + 22 5 y = − 2 5 x + 22 5

y = 1 3 x − 10 3 y = 1 3 x − 10 3

y = − 2 5 x − 23 5 y = − 2 5 x − 23 5

x = 5 x = 5

x = −4 x = −4

y = 3 x − 10 y = 3 x − 10

y = 1 2 x + 1 y = 1 2 x + 1

y = − 1 3 x + 10 3 y = − 1 3 x + 10 3

y = −2 x + 16 y = −2 x + 16

y = −5 y = −5

y = −1 y = −1

x = −5 x = −5

ⓐ yes ⓑ yes ⓒ yes ⓓ yes ⓔ no

ⓐ yes ⓑ yes ⓒ no ⓓ no ⓔ yes

y ≥ −2 x + 3 y ≥ −2 x + 3

y < 1 2 x − 4 y < 1 2 x − 4

x − 4 y ≤ 8 x − 4 y ≤ 8

3 x − y ≤ 6 3 x − y ≤ 6

Section 4.1 Exercises

A: ( −4 , 1 ) ( −4 , 1 ) B: ( −3 , −4 ) ( −3 , −4 ) C: ( 1 , −3 ) ( 1 , −3 ) D: ( 4 , 3 ) ( 4 , 3 )

A: ( 0 , −2 ) ( 0 , −2 ) B: ( −2 , 0 ) ( −2 , 0 ) C: ( 0 , 5 ) ( 0 , 5 ) D: ( 5 , 0 ) ( 5 , 0 )

ⓑ Age and weight are only positive.

Section 4.2 Exercises

ⓐ yes; no ⓑ no; no ⓒ yes; yes ⓓ yes; yes

ⓐ yes; yes ⓑ yes; yes ⓒ yes; yes ⓓ no; no

$722, $850, $978

Section 4.3 Exercises

( 3 , 0 ) , ( 0 , 3 ) ( 3 , 0 ) , ( 0 , 3 )

( 5 , 0 ) , ( 0 , −5 ) ( 5 , 0 ) , ( 0 , −5 )

( −2 , 0 ) , ( 0 , −2 ) ( −2 , 0 ) , ( 0 , −2 )

( −1 , 0 ) , ( 0 , 1 ) ( −1 , 0 ) , ( 0 , 1 )

( 6 , 0 ) , ( 0 , 3 ) ( 6 , 0 ) , ( 0 , 3 )

( 0 , 0 ) ( 0 , 0 )

( 4 , 0 ) , ( 0 , 4 ) ( 4 , 0 ) , ( 0 , 4 )

( −3 , 0 ) , ( 0 , 3 ) ( −3 , 0 ) , ( 0 , 3 )

( 8 , 0 ) , ( 0 , 4 ) ( 8 , 0 ) , ( 0 , 4 )

( 2 , 0 ) , ( 0 , 6 ) ( 2 , 0 ) , ( 0 , 6 )

( 12 , 0 ) , ( 0 , −4 ) ( 12 , 0 ) , ( 0 , −4 )

( 2 , 0 ) , ( 0 , −8 ) ( 2 , 0 ) , ( 0 , −8 )

( 5 , 0 ) , ( 0 , 2 ) ( 5 , 0 ) , ( 0 , 2 )

( 4 , 0 ) , ( 0 , −6 ) ( 4 , 0 ) , ( 0 , −6 )

( 3 , 0 ) , ( 0 , 1 ) ( 3 , 0 ) , ( 0 , 1 )

( −10 , 0 ) , ( 0 , 2 ) ( −10 , 0 ) , ( 0 , 2 )

ⓐ ( 0 , 1000 ) , ( 15 , 0 ) ( 0 , 1000 ) , ( 15 , 0 ) ⓑ At ( 0 , 1000 ) ( 0 , 1000 ) , he has been gone 0 hours and has 1000 miles left. At ( 15 , 0 ) ( 15 , 0 ) , he has been gone 15 hours and has 0 miles left to go.

Section 4.4 Exercises

−3 2 = − 3 2 −3 2 = − 3 2

− 1 3 − 1 3

− 3 4 − 3 4

− 5 2 − 5 2

− 8 7 − 8 7

ⓐ 1 3 1 3 ⓑ 4 12 pitch or 4-in-12 pitch

3 50 3 50 ; rise = 3, run = 50

ⓐ 288 inches (24 feet) ⓑ Models will vary.

When the slope is a positive number the line goes up from left to right. When the slope is a negative number the line goes down from left to right.

A vertical line has 0 run and since division by 0 is undefined the slope is undefined.

Section 4.5 Exercises

slope m = 4 m = 4 and y -intercept ( 0 , −2 ) ( 0 , −2 )

slope m = −3 m = −3 and y -intercept ( 0 , 1 ) ( 0 , 1 )

slope m = − 2 5 m = − 2 5 and y -intercept ( 0 , 3 ) ( 0 , 3 )

−9 ; ( 0 , 7 ) −9 ; ( 0 , 7 )

4 ; ( 0 , −10 ) 4 ; ( 0 , −10 )

−4 ; ( 0 , 8 ) −4 ; ( 0 , 8 )

− 8 3 ; ( 0 , 4 ) − 8 3 ; ( 0 , 4 )

7 3 ; ( 0 , −3 ) 7 3 ; ( 0 , −3 )

horizontal line

vertical line

slope–intercept

ⓒ The slope, 2.54, means that Randy’s payment, P , increases by $2.54 when the number of units of water he used, w, increases by 1. The P –intercept means that if the number units of water Randy used was 0, the payment would be $28.
ⓒ The slope, 0.32, means that the cost, C , increases by $0.32 when the number of miles driven, m, increases by 1. The C -intercept means that if Janelle drives 0 miles one day, the cost would be $15.
ⓒ The slope, 0.09, means that Patel’s salary, S , increases by $0.09 for every $1 increase in his sales. The S -intercept means that when his sales are $0, his salary is $750.
ⓒ The slope, 42, means that the cost, C , increases by $42 for when the number of guests increases by 1. The C -intercept means that when the number of guests is 0, the cost would be $750.

not parallel

ⓐ For every increase of one degree Fahrenheit, the number of chirps increases by four.
ⓑ There would be −160 −160 chirps when the Fahrenheit temperature is 0 ° 0 ° . (Notice that this does not make sense; this model cannot be used for all possible temperatures.)

Section 4.6 Exercises

y = 4 x + 1 y = 4 x + 1

y = 8 x − 6 y = 8 x − 6

y = − x + 7 y = − x + 7

y = −3 x − 1 y = −3 x − 1

y = 1 5 x − 5 y = 1 5 x − 5

y = − 2 3 x − 3 y = − 2 3 x − 3

y = 2 y = 2

y = −4 x y = −4 x

y = −2 x + 4 y = −2 x + 4

y = 3 4 x + 2 y = 3 4 x + 2

y = − 3 2 x − 1 y = − 3 2 x − 1

y = 6 y = 6

y = 3 8 x − 1 y = 3 8 x − 1

y = 5 6 x + 2 y = 5 6 x + 2

y = − 3 5 x + 1 y = − 3 5 x + 1

y = − 1 3 x − 11 y = − 1 3 x − 11

y = −7 y = −7

y = − 5 2 x − 22 y = − 5 2 x − 22

y = −4 x − 11 y = −4 x − 11

y = −8 y = −8

y = −4 x + 13 y = −4 x + 13

y = x + 5 y = x + 5

y = − 1 3 x − 14 3 y = − 1 3 x − 14 3

y = 7 x + 22 y = 7 x + 22

y = − 6 7 x + 4 7 y = − 6 7 x + 4 7

y = 1 5 x − 2 y = 1 5 x − 2

x = 4 x = 4

x = −2 x = −2

y = −3 y = −3

y = 4 x y = 4 x

y = 1 2 x + 3 2 y = 1 2 x + 3 2

y = 5 y = 5

y = 3 x − 1 y = 3 x − 1

y = −3 x + 3 y = −3 x + 3

y = 2 x − 6 y = 2 x − 6

y = − 2 3 x + 5 y = − 2 3 x + 5

x = −3 x = −3

y = −4 y = −4

y = x y = x

y = − 3 4 x − 1 4 y = − 3 4 x − 1 4

y = 5 4 x y = 5 4 x

y = 1 y = 1

y = x + 2 y = x + 2

y = 3 4 x y = 3 4 x

y = 1.2 x + 5.2 y = 1.2 x + 5.2

Section 4.7 Exercises

ⓐ yes ⓑ no ⓒ no ⓓ yes ⓔ no

ⓐ yes ⓑ no ⓒ no ⓓ yes ⓔ yes

ⓐ no ⓑ no ⓒ no ⓓ yes ⓔ yes

y < 2 x − 4 y < 2 x − 4

y ≤ − 1 3 x − 2 y ≤ − 1 3 x − 2

x + y ≥ 3 x + y ≥ 3

x + 2 y ≥ −2 x + 2 y ≥ −2

2 x − y < 4 2 x − y < 4

4 x − 3 y > 12 4 x − 3 y > 12

ⓑ Answers will vary.

Review Exercises

ⓐ yes; yes ⓑ yes; no

( 6 , 0 ) , ( 0 , 4 ) ( 6 , 0 ) , ( 0 , 4 )

− 1 2 − 1 2

slope m = − 2 3 m = − 2 3 and y -intercept ( 0 , 4 ) ( 0 , 4 )

5 3 ; ( 0 , −6 ) 5 3 ; ( 0 , −6 )

4 5 ; ( 0 , − 8 5 ) 4 5 ; ( 0 , − 8 5 )

plotting points

ⓐ −$250 ⓑ $450 ⓒ The slope, 35, means that Marjorie’s weekly profit, P , increases by $35 for each additional student lesson she teaches. The P –intercept means that when the number of lessons is 0, Marjorie loses $250. ⓓ

y = −5 x − 3 y = −5 x − 3

y = −2 x y = −2 x

y = −3 x + 5 y = −3 x + 5

y = 3 5 x y = 3 5 x

y = −2 x − 5 y = −2 x − 5

y = 1 2 x − 5 2 y = 1 2 x − 5 2

y = − 2 5 x + 8 y = − 2 5 x + 8

y = 3 y = 3

y = − 3 2 x − 6 y = − 3 2 x − 6

y > 2 3 x − 3 y > 2 3 x − 3

x − 2 y ≥ 6 x − 2 y ≥ 6

Practice Test

( 3 , 0 ) , ( 0 , −4 ) ( 3 , 0 ) , ( 0 , −4 )

y = − 3 4 x − 2 y = − 3 4 x − 2

y = 1 2 x − 4 y = 1 2 x − 4

y = − 4 5 x − 5 y = − 4 5 x − 5

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$Go Math Answer Key$

Texas Go Math Grade 8 Lesson 4.2 Answer Key Determining Slope and y-Intercept

Refer to our Texas Go Math Grade 8 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 8 Lesson 4.2 Answer Key Determining Slope and y-Intercept.

Essential Question How can you determine the slope and the y-intercept of a line?

Texas Go Math Grade 8 Lesson 4.2 Explore Activity Answer Key

Investigating Slope and y-intercept The graph of every nonvertical line crosses the y-axis. The y-intercept is the y-coordinate of the point where the graph intersects the y-axis. The x-coordinate of this point is always 0.

The graph represents the linear equation y = –$\frac{2}{3}$ + 4.

$Texas Go Math Grade 8 Lesson 4.2 Answer Key 1$

Step 2 The line also contains the point (6, 0). What is the slope using (0, 4) and (6, 0)? Using (-3, 6) and (6, 0). What do you notice?

Step 3 Compare your answers in Steps 1 and 2 with the equation of the graphed line.

Step 4 Find the value of y when x = 0 using the equation y = –$\frac{2}{3}$x + 4. Describe the point on the graph that corresponds to this solution.

Step 5 Compare your answer in Step 3 with the equation of the line.

Find the slope and y-intercept of the line represented by each table.

$Texas Go Math Grade 8 Lesson 4.2 Answer Key 3$

Explore Activity 2

Deriving the Slope-intercept Form of an Equation

In the following Explore Activity, you will derive the slope-intercept form of an equation.

Step 1 Let L be a line with slope m and y-intercept b. Circle the point that must be on the line. Justify your choice. (b, 0) (0, b) (0, m) (m, 0)

$Texas Go Math Grade 8 Lesson 4.2 Answer Key 5$

Question 3. Critical Thinking Write the equation of a line with slope m that passes through the origin. Explain your reasoning. Answer: y= x When the line passes through the origin, y-intercept = 0 in y = mx + b

Texas Go Math Grade 8 Lesson 4.2 Guided Practice Answer Key

Find the slope and y-intercept of the line in each graph. (Explore Activity 1)

$Texas Go Math Grade 8 Lesson 4.2 Answer Key 7$

According to the equation y = mx + b we can calculate the y-intercept, that is b. Include the values of x and y from one point and the obtained slope value y = mx + b -1 = -2 . 0 + b b = 1 – 0 b = 1

$Texas Go Math Grade 8 Lesson 4.2 Answer Key 8$

According to the equation y = mx + b we can calculate the y-intercept, that is b. Include the values of x and y from one point and the obtained slope value. y = mx + b -2 = $\frac{3}{2}$ . 0 + b -2 = 0 + b b = -2

$Texas Go Math Grade 8 Lesson 4.2 Answer Key 10$

According to the equation y = mx + b we can calculate the y-intercept, that is b. Include the values of x and y from one point and the obtained slope value. y = mx + b 9 = -3 . 0 + b 9 = 0 + b b = 9

Find the slope and y-intercept of the line represented by each table. (Example 1)

$Texas Go Math Grade 8 Lesson 4.2 Answer Key 11$

Essential Question Check-In

Go Math Answer Key Grade 8 Lesson 4.2 Determining Slope and Y-Intercept Question 7. How can you determine the slope and the y-intercept of a line from a graph? Answer: Choose any two points on the line from the graph and use it to find the slope. Determine the point where the line crosses the y-axis to find the y-intercept.

Texas Go Math Grade 8 Lesson 4.2 Independent Practice Answer Key

$Texas Go Math Grade 8 Lesson 4.2 Answer Key 13$

The slope is calculated by: m = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

The first point is (1, 125) and the second point is (2, 175). Put those in the calculation: m = $\frac{175-125}{2-1}$ = $\frac{50}{1}$ = 50 The standard form of our Linear function is y = mx – 1- b We need to get the initial value of this function. Take a look at the equation, compare the data we already have, and find what we need to get. Thus, the y-intercept (”b”) is unknown.

Include the values of x, y, and the slope in the equation and calculate: y = mx + b 125 = 50 . 1 + b 125 = 50 + b b = 125 – 50 b = 75

Lesson 4.2 Slope of a Line Answer Key Go Math 8th Grade Pdf Question 9. Make Predictions The total cost to pay for parking at a state park for the day and rent a paddleboat are shown.

a. Find the cost to park for a day and the hourly rate to rent a paddleboat. Answer: Slope = $\frac{29-17}{2-1}$ = $\frac{12}{1}$ = 12 Finding the slope using any two given points by Slope(m) = (y 2 – y 2 ) ÷ (x 2 – x 1 ) where (x 2 , y 2 ) = (2, 29) and (x 1 , y 1 ) = (1, 17) The hourly rent is $\$12$ per hr

Work backward from x = 1 to x = 0 Find the initial value when the value of x is 0 $\frac{29-17}{2-1}$ = $\frac{12}{1}$ x = 1 1 = 0 Subtract the difference of x and y from the first point. y = 17 – 12 = 5 The cost to park for a day is $\$5$

$Texas Go Math Grade 8 Lesson 4.2 Answer Key 14$

b. What will Lin pay if she rents a paddleboat for 3.5 hours and splits the total cost with a friend? Explain. Answer: Total Cost = 3.5(12) + 5 = 47 When Lin paddles for 3.5 hr Lin’s Cost = $\frac{47}{2}$ = 23.5

$Texas Go Math Grade 8 Lesson 4.2 Answer Key 15$

b. Find the rate of change and the initial value for the private lessons. Answer: Slope = $\frac{125-75}{2-1}$ = $\frac{50}{1}$ = 50 Finding the slope using any two given points by slope (m) = (y 2 – y 1 ) ÷ (x 2 – x 1 ) Rate of change is $\$50$ per lesson where (x 2 , y 2 ) = (2, 125) and (x 1 , y 1 ) = (1, 75) Work backward from x = 1 to x = 0 Find the initial value when the value of x is 0 $\frac{125-75}{2-1}$ = $\frac{50}{1}$ x = 1 – 1 = 0 Subtract the difference of x and y from the first point y = 75 – 50 = 25 The initial value of group lessons is $\$25$

c. Compare and contrast the rates of change and the initial values. Answer: The initial value for both types of lessons is the same. Comparing results from parts a and b. The rate of change is higher for private lessons than group lessons.

Vocabulary Explain why each relationship is not linear.

$Texas Go Math Grade 8 Lesson 4.2 Answer Key 16$

Question 13. Communicate Mathematical Ideas Describe the procedure you performed to derive the slope-intercept form of a linear equation. (Explore Activity 2) Answer: Express the slope m between a random point (x, y) on the line and the point (0, b) where the line crosses the y-axis. Then solve the equation for y.

Texas Go Math Grade 8 Lesson 4.2 H.O.T. Focus On Higher Order Thinking Answer Key

Question 14. Critique Reasoning Your teacher asked your class to describe a real-world situation in which the y-intercept is 100 and the slope is 5. Your partner gave the following description: My younger brother originally had 100 small building blocks, but he has lost 5 of them every month since.

a. What mistake did your partner make? Answer: a. If the brother loses 5 blocks every month, the slope would be -5 and not 5. When the initial value is decreasing, the slope is negative.

b. Describe a real-world situation that does match the situation. Answer: I bought a 1oo card pack and bought 5 additional cards every month. Real-world situation

$Texas Go Math Grade 8 Lesson 4.2 Answer Key 18$

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Worksheet on Point Slope Form | Point Slope Form Practice Worksheet with Answers

The worksheet on Point-Slope Form consists of all Point Slope Form Problems with Answers related to finding the equation of a line using the point-slope form method. Solve all the Point-Slope problems with Solutions on your own to know how to find the equation of a line. Different tricks and tips are also included in this Point Slope Form Practice Worksheet PDF for easy solving of questions.

So, first, quickly go through the entire article and gain a high knowledge of point-slope form word problems as well. The complete information about finding the equation of a line using a point-slope form is given in this Worksheet for 10th Grade Math PDF articles. This Point Slope Form Worksheet with Answers PDF will help students to solve problems easily.

Also, Read:

Point Slope Form of Line
Equation of a Straight Line

Point-Slope Form Quiz PDF

Check out the below problems to learn the Point-slope form concepts deeply. The different problems along with their answers are given below.

Problem 1: Find the equation of a line that passes through (-2, 5) and with a slope is -8.

Given that, The points (x 1 ,y 1 ) are (-2,5). The slope of a line i.e., m = -8. We know the formula of the equation of a line using a point-slope form is, (y-y 1 ) = m(x-x 1 ) Now place the given values in the above formula. It will be, y-(5) = (−8)(x − (-2)) i.e., y-5 = -8x -16 8x+y-5 +16 =0 8x+y+11 =0 Hence, the equation of the line is 8x+y+11 =0.

Problem 2: Find the equation of a line that passes through the points (4, –2) and (1, 4) in point-slope form.

In the given question, The points (x 1 ,y 1 ) is (4, -2). The points of (x 2 ,y 2 )are (1, 4). The slope of the line that passes through the points formula is m = (y 2 – y 1 )/ (x 2 – x 1 ) Now place the given values in the above formula. Then it will be m = (4-(-2))/(1-4) m= 6/-3 So, the slope of the line m is -2. Next, the equation of a line which is passing through the point (4, -2) with a slope is -2. We all know the formula for equation of a line using point-slope form is, (y-y 1 ) = m(x- x 1 ) y -(-2) = -2(x – 4) y + 2 = -2x +8 2x + y + 2 – 8 = 0 2x + y -6 = 0 Similarly, the equation of a line passing through the point (1, 4) with slope of a line -2. Place these value in a point slope from formula. Then we get, y – 4 = -2(x – 1) y – 4 = -2x +2 2x + y – 4 -2= 0 2x + y -6 = 0 Therefore, the equation of the line in point slope form is 2x + y – 6 = 0.

Problem 3: A straight line that passes through the point (8, -5), and the positive direction of the x-axis gives an angle of 135°. Find the equation for a straight line?

As given in the question, The points ( x 1 , y 1 ) are (8,-5) An angle of 135 ° with a positive direction of the x-axis line. The slope of the line m is, m= tan 135 ° = tan (90 ° + 45 °) = – cot 45 ° = -1. The line that is needed to pass through the point (8, -5). We know the equation of a line using the point-slope formula. So, the formula is (y- y 1 ) = m(x- x 1 ) Substitute the values in the above formula. We get, y – (-5) = -1 (x -8) y + 5 = -x + 8 x + y + 5- 8 = 0 x + y -3 = 0 Thus, the equation of a straight line is x + y – 3 = 0.

Problem 4: What is the value of the slope of the line when the equation of the line is 5x-7y +1.

Given that, the equation of a line is 5x-7y+1 Now, we will find the value of the slope of a line. The given equation of a line is in the form of ax + by + c is -a/b So, the value of a is 5 and the value of b is -7. Then the value of the m is -(5/-7) Hence, the slope of a line is 5/7.

Problem 5: Find the line equation with a slope of -1/3 and go through the points (4, -6)?

In the given question, The points ( x 1 , y 1 ) are (4,-6) The slope of the line m is -1/3. We know the formula of the equation of a line using a point-slope form is, (y-y 1 ) = m(x-x 1 ) After placing the given values in the above formula. It will be, y-(-6) = (−1/3)(x −4) i.e., 3(y+6) =(-1)(x -4) 3y+18=-x+4 x+3y-4 +18 =0 x+3y+14 =0 Hence, the equation of the line according to the point-slope form is x+3y+14 =0.

Problem 6: Find the equation of a straight line whose inclination is 60° and which passes through the point (0, – 3).

In the given question, The equation of a line passes through the points are (0,-3) = ( x 1 , y 1 ) The inclination of a straight line is 60°. First, find the slope of a line ‘m’ value. So, the slope of a line is tan 60° = √3. We know the formula of an equation of a line using the point-slope form is, (y-y 1 ) = m(x-x 1 ) After putting the given values in the above formula. It will be, y-(-3) = (√3)(x −0) y + 3 = √3 (x – 0) y + 3 = √3x √3x – y – 3 = 0 Therefore, the required equation of a line is √3x – y – 3 = 0.

Problem 7: Find the equation of the straight line with slope -1 and the y-intercept is 6?

Given that, The slope of the line is -1 i.e., m = -1. The y-intercept value is 3. This means the line cuts the y-axis on the fixed point (0, 3). So, the points (x 1 , y 1 ) are (0, 6). The formula for point-slope of line is (y-y 1 ) = m(x-x 1 ). Now substitute the values of m, x, and y in the formula. y – 6 = (-1)(x – 0) y – 6 = (-1)x y – 6 = -x We will get the equation is y + x – 6 = 0 So, the required equation of a line is x+y-6 = 0.

Problem 8: What is the equation of the straight line whose slope of a line is -3 and the x-intercept is -8?

As given in the question, The slope of the line is -3 i.e., m = -3. The x-intercept is -7. This means the (x 1 , y 1 ) value is (-7,0). Now, Put the values of m and (x 1 , y 1 ) in the point-slope form formula. The formula is (y-y 1 ) = m(x-x 1 ). After substituting the value, we get y-y 1 = (-3)(x –(-7)) y-y 1 = (-3)(x + 7) y-0 = -3x – 21 y + 3x + 21 = 0 Hence, the required equation is 3x+y+21= 0.

Problem 9: What is the equation of a line which is passing through the points (8, –4) and (5, 10) in point-slope form.

In the given question, The points (x 1 ,y 1 ) is (8, -4). The points of (x 2 ,y 2 )are (6, 10). The slope of the line which is passing through the points formula is, m = (y 2 – y 1 )/ (x 2 – x 1 ) After placing the given values in the above formula. Then we get, m = (10-(-4))/(6-8) m= 14/-2 So, the slope of the line m is -7. The equation of a line passing through the point (8, -4) with slope -7. The equation of a line using point-slope form formula is, (y-y 1 ) = m(x- x 1 ) y -(-4) = -7(x – 8) y + 4 = -7x +56 7x + y + 4 – 56= 0 7x + y -52 = 0 Similarly, the equation of a line passing through the point (6, 10) with slope of a line -7. Substitute the value in a point-slope formula. Then we get, y – 10 = -7(x – 6) y – 10 = -7x +42 7x + y – 10 – 42= 0 7x + y -52 = 0 Therefore, the equation of the line using the point-slope form is 7x + y – 52 = 0.

Problem 10: The equation of the line passing through (1, 3) and making an angle of 30° in a clockwise direction with the positive direction of the y-axis.

As given in the question, The points (x 1 ,y 1 ) is (1,3) The line makes an angle of 30° in a clockwise direction with the positive direction of the y-axis. It will make an angle of 60° in an anti-clockwise direction with the positive direction of the x-axis. Now, we need to find out the value of the slope of a line and the equation of a line. The slope of the line m = tan 60° = √3. The equation of a line using point-slope form formula is (y-y 1 ) = m(x- x 1 ) Substitute the values (1,2) and slope value √3 in formula. Then we get, y−3=√3(x−1) y-3= √3x-√3 √3x−y+3-√3 = 0. Therefore, the required equation of a straight line is √3x−y+3-√3 = 0.