Students can use the Spectrum Math Grade 8 Answer Key Chapter 3 Lesson 3.2 Graphing Linear Equations Using Slope 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)
Any line can be graphed using two 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)
Any line can be graphed using two 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)
Any line can be graphed using two 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)
Any line can be graphed using two 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 • 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 • 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 • 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 • 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 • 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: 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