# Spectrum Math Grade 8 Chapter 3 Lesson 2 Answer Key Graphing Linear Equations Using Slope

Students can use the Spectrum Math Grade 8 Answer Key Chapter 3 Lesson 3.2 Graphing Linear Equations Using SlopeĀ 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

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

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

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

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
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
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
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

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