Students can use the **Spectrum Math Grade 8 Answer Key** **Chapter 3 Lesson 3.2 Graphing Linear Equations Using Slope**Ā as a quick guide to resolve any of their doubts.

## Spectrum Math Grade 8 Chapter 3 Lesson 3.2 Graphing Linear Equations Using Slope Answers Key

If the slope of a line and the place it intercepts (or crosses) the y-axis are known, a line can be graphed using an equation with x and y variables.

Step 1: Find the point where the line crosses the y-axis. (0, 5)

Step 2: Find the slope: -2.

In fraction form, the slope is \(\frac{-2}{1}\).

Step 3: Starting at the intercept, mark the slope by using the numerator to count along the y-axis, and the denominator to count along the x-axis: Move down 2, and to the right 1.

Step 4: Draw a line to connect the points.

**Use the slope-intercept form of equations to draw lines on the grids below.**

Question 1.

a.

y = \(\frac{1}{4}\)x + 1

Answer:

From the given slope-intercept equation, find out the slope and y-intercept

Slope = \(\frac{1}{4}\)

Y-intercept = (0,1)

AnyĀ lineĀ can be graphed using twoĀ points. select the other point using slope and y-intercept in order to plot the graph.

The other point would be (4,2)

b. y = -x + 2

Answer:

From the given slope-intercept equation, find out the slope and y-intercept

Slope = -1

Y-intercept = (0,2)

AnyĀ lineĀ can be graphed using twoĀ points. select the other point using slope and y-intercept in order to plot the graph.

The other point would be (1,1)

Question 2.

a.

y = \(\frac{4}{3}\)x + 4

Answer:

From the given slope-intercept equation, find out the slope and y-intercept

Slope = \(\frac{4}{3}\)

Y-intercept = (0,4)

AnyĀ lineĀ can be graphed using twoĀ points. select the other point using slope and y-intercept in order to plot the graph.

The other point would be (3,8)

b. y = 2x + 3

Answer:

From the given slope-intercept equation, find out the slope and y-intercept

Slope =2

Y-intercept = (0,3)

AnyĀ lineĀ can be graphed using twoĀ points. select the other point using slope and y-intercept in order to plot the graph.

The other point would be (1,5)

When a linear equation is graphed, the equation that was used to create the line can be found by using the slope-intercept equation.

Step 1: Find the point where the line crosses the y-axis. (0, 2)

Step 2: Mark points on the line where it crosses at exact locations that correspond to an ordered pair.

(5, 4) and (10, 6)

Step 3: Calculate the slope using

Step 4: Use y = slope ā¢ x + intercept to create the equation for the line in slope-intercept form.

y = \(\frac{2}{5}\)x + 2

**Use the pictures below to create equations for the lines in slope-intercept form.**

Question 1.

a.

Answer: y = -1x + 7

Step 1: Find the point where the line crosses the y-axis. (0, 7)

Step 2: Mark points on the line where it crosses at exact locations that correspond to an ordered pair.

(2,5) and (7,0)

Step 3: Calculate the slope using \(\frac{change in y}{change in x}\) = \(\frac{5 – 7}{2-0}\) = \(\frac{-2}{2}\) = -1

Step 4: Use y = slope ā¢ x + intercept to create the equation for the line in slope-intercept form.

y = -1x + 7

b.

Answer: y = \(\frac{1}{2}\)x + 7

Step 1: Find the point where the line crosses the y-axis. (0, 4)

Step 2: Mark points on the line where it crosses at exact locations that correspond to an ordered pair.

(2,5) and (10,9)

Step 3: Calculate the slope using \(\frac{change in y}{change in x}\) = \(\frac{5 – 4}{2-0}\) = \(\frac{1}{2}\)

Step 4: Use y = slope ā¢ x + intercept to create the equation for the line in slope-intercept form.

y = \(\frac{1}{2}\)x + 7

Question 2.

a.

Answer: y =\(\frac{-3}{2}\)x + 7

Step 1: Find the point where the line crosses the y-axis. (0, 6)

Step 2: Mark points on the line where it crosses at exact locations that correspond to an ordered pair.

(2,3) and (4,0)

Step 3: Calculate the slope using \(\frac{change in y}{change in x}\) = \(\frac{3-6}{2-0}\) = \(\frac{-3}{2}\)

Step 4: Use y = slope ā¢ x + intercept to create the equation for the line in slope-intercept form.

y =\(\frac{-3}{2}\)x + 7

b.

Answer: y = \(\frac{2}{3}\)x + 7

Step 1: Find the point where the line crosses the y-axis. (0, 0)

Step 2: Mark points on the line where it crosses at exact locations that correspond to an ordered pair.

(3,2) and (9,6)

Step 3: Calculate the slope using \(\frac{change in y}{change in x}\) = \(\frac{2-0}{3-0}\) = \(\frac{2}{3}\)

Step 4: Use y = slope ā¢ x + intercept to create the equation for the line in slope-intercept form.

y = \(\frac{2}{3}\)x + 7

When given the slope and intercept of any straight line, a linear equation can be created using the slope-intercept form.

Slope: \(\frac{5}{6}\); Intercept: -2

Step 1: Use the equation y = mx + b, where m equals slope and b is the y-intercept.

Step 2: Substitute the known quantities for the slope and the y-intercept.

y = \(\frac{5}{6}\)x – 2

**Use slope-intercept form to write equations given the conditions below.**

Question 1.

a. slope: \(\frac{4}{3}\); intercept: 3

Answer: y = \(\frac{4}{3}\)x +3

slope: \(\frac{4}{3}\); intercept: 3

Step 1: Use the equation y = mx + b, where m equals slope and b is the y-intercept.

Step 2: Substitute the known quantities for the slope and the y-intercept.

y = \(\frac{4}{3}\)x +3

b. slope: -2; intercept: 4

Answer: y = -2x +4

slope: -2; intercept: 4

Step 1: Use the equation y = mx + b, where m equals slope and b is the y-intercept.

Step 2: Substitute the known quantities for the slope and the y-intercept.

y = -2x +4

c. slope: –\(\frac{1}{2}\); intercept: 7

Answer: y = –\(\frac{1}{2}\)x + 7

slope: –\(\frac{1}{2}\); intercept: 7

Step 1: Use the equation y = mx + b, where m equals slope and b is the y-intercept.

Step 2: Substitute the known quantities for the slope and the y-intercept.

y = –\(\frac{1}{2}\)x + 7

Question 2.

a. slope: 3; intercept: -5

Answer: y =3x -5

slope: 3; intercept: -5

Step 1: Use the equation y = mx + b, where m equals slope and b is the y-intercept.

Step 2: Substitute the known quantities for the slope and the y-intercept.

y =3x -5

b. slope: \(\frac{2}{5}\); intercept: 0

Answer: y =\(\frac{2}{5}\)x

slope: \(\frac{2}{5}\); intercept: 0

Step 1: Use the equation y = mx + b, where m equals slope and b is the y-intercept.

Step 2: Substitute the known quantities for the slope and the y-intercept.

y =\(\frac{2}{5}\)x +0

y =\(\frac{2}{5}\)x

c. slope: –\(\frac{3}{4}\); intercept: -2

Answer: y = –\(\frac{3}{4}\)x -2

slope: –\(\frac{3}{4}\); intercept: -2

Step 1: Use the equation y = mx + b, where m equals slope and b is the y-intercept.

Step 2: Substitute the known quantities for the slope and the y-intercept.

y = –\(\frac{3}{4}\)x -2

Question 3.

a. slope: -4; intercept: 6

Answer: y = -4x+6

slope: -4; intercept: 6

Step 1: Use the equation y = mx + b, where m equals slope and b is the y-intercept.

Step 2: Substitute the known quantities for the slope and the y-intercept.

y = -4x+6

b. slope: \(\frac{5}{2}\); intercept: -3

Answer:Ā y = \(\frac{5}{2}\)x-3

slope: \(\frac{5}{2}\); intercept: -3

Step 1: Use the equation y = mx + b, where m equals slope and b is the y-intercept.

Step 2: Substitute the known quantities for the slope and the y-intercept.

y = \(\frac{5}{2}\)x-3

c. slope: \(\frac{1}{2}\); intercept: 1

Answer: y = \(\frac{1}{2}\)x+1

slope: \(\frac{1}{2}\); intercept: 1

Step 1: Use the equation y = mx + b, where m equals slope and b is the y-intercept.

Step 2: Substitute the known quantities for the slope and the y-intercept.

y = \(\frac{1}{2}\)x+1