3.2 Slope of a Line

Rise over run from a graph or from two points, sketching directly from slope-intercept form, and testing whether two lines are parallel or perpendicular.

Intermediate Algebra 2e, 3.2 Slope of a Line

Status

FlagsLoading your progress…

47 exercises

3.2 Exercise 1

Before you get started, take this readiness quiz.

Simplify: $\frac{\left(1 – 4\right)}{\left(8 - 2\right)} .$
If you missed this problem, review the reference.

2.5

3.2 Exercise 2

Divide: $\frac{0}{4} , \frac{4}{0} .$
If you missed this problem, review the reference.

2.5

3.2 Exercise 3

Simplify: $\frac{15}{−3} , \frac{−15}{3} , \frac{−15}{−3} .$
If you missed this problem, review the reference.

2.5

3.2 Exercise 7

Find the slope of each line: ⓐ $x = 8$ ⓑ $y = −5 .$

2.5

3.2 Exercise 8

Find the slope of the line: $x = −4 .$

2.5

3.2 Exercise 9

Find the slope of the line: $y = 7 .$

2.5

3.2 Exercise 11

Use the slope formula to find the slope of the line through the pair of points: $\left(−3 , 4\right)$ and $\left(2 , −1\right) .$

2.5

3.2 Exercise 12

Use the slope formula to find the slope of the line through the pair of points: $\left(−2 , 6\right)$ and $\left(−3 , −4\right) .$

2.5

3.2 Exercise 17

Identify the slope and y-intercept from the equation of the line.

ⓐ $y = \frac{2}{5} x - 1$ ⓑ $x + 4 y = 8$

2.5

3.2 Exercise 18

Identify the slope and y-intercept from the equation of the line.

ⓐ $y = - \frac{4}{3} x + 1$ ⓑ $3 x + 2 y = 12$

2.5

3.2 Exercise 22

Determine the most convenient method to graph each line:

ⓐ $y = 5$ ⓑ $4 x - 5 y = 20$ ⓒ $x = −3$ ⓓ $y = - \frac{5}{9} x + 8$

2.5

3.2 Exercise 23

Determine the most convenient method to graph each line:

ⓐ $3 x + 2 y = 12$ ⓑ $y = 4$ ⓒ $y = \frac{1}{5} x - 4$ ⓓ $x = −7 .$

2.5

3.2 Exercise 24

Determine the most convenient method to graph each line:

ⓐ $x = 6$ ⓑ $y = - \frac{3}{4} x + 1$ ⓒ $y = −8$ ⓓ $4 x - 3 y = −1 .$

2.5

3.2 Exercise 31

Use slopes and y-intercepts to determine if the lines are parallel:

ⓐ $3 x - 2 y = 6$ and $y = \frac{3}{2} x + 1$ ⓑ $y = 2 x - 3$ and $−6 x + 3 y = −9 .$

2.5

3.2 Exercise 32

Use slopes and y-intercepts to determine if the lines are parallel:

ⓐ $2 x + 5 y = 5$ and $y = - \frac{2}{5} x - 4$ ⓑ $y = - \frac{1}{2} x - 1$ and $x + 2 y = −2 .$

2.5

3.2 Exercise 33

Use slopes and y-intercepts to determine if the lines are parallel:

ⓐ $4 x - 3 y = 6$ and $y = \frac{4}{3} x - 1$ ⓑ $y = \frac{3}{4} x - 3$ and $3 x - 4 y = 12 .$

2.5

3.2 Exercise 34

Use slopes and y-intercepts to determine if the lines are parallel:

ⓐ $y = −4$ and $y = 3$ ⓑ $x = −2$ and $x = −5 .$

2.5

3.2 Exercise 35

Use slopes and y-intercepts to determine if the lines are parallel:

ⓐ $y = 8$ and $y = −6$ ⓑ $x = 1$ and $x = −5 .$

2.5

3.2 Exercise 36

Use slopes and y-intercepts to determine if the lines are parallel:

ⓐ $y = 1$ and $y = −5$ ⓑ $x = 8$ and $x = −6 .$

2.5

3.2 Exercise 37

Use slopes to determine if the lines are perpendicular:

ⓐ $y = −5 x - 4$ and $x - 5 y = 5$ ⓑ $7 x + 2 y = 3$ and $2 x + 7 y = 5$

2.5

3.2 Exercise 38

Use slopes to determine if the lines are perpendicular:

ⓐ $y = −3 x + 2$ and $x - 3 y = 4$ ⓑ $5 x + 4 y = 1$ and $4 x + 5 y = 3 .$

2.5

3.2 Exercise 39

Use slopes to determine if the lines are perpendicular:

ⓐ $y = 2 x - 5$ and $x + 2 y = −6$ ⓑ $2 x - 9 y = 3$ and $9 x - 2 y = 1 .$

2.5

3.2 Exercise 48

Find the slope of each line.

$y = 3$

2.5

3.2 Exercise 50

Find the slope of each line.

$x = −5$

2.5

3.2 Exercise 52

Use the slope formula to find the slope of the line between each pair of points.

$\left(2 , 5\right) , \left(4 , 0\right)$

2.5

3.2 Exercise 54

Use the slope formula to find the slope of the line between each pair of points.

$\left(−3 , 3\right) , \left(4 , −5\right)$

2.5

3.2 Exercise 56

Use the slope formula to find the slope of the line between each pair of points.

$\left(−1 , −2\right) , \left(2 , 5\right)$

2.5

3.2 Exercise 58

Use the slope formula to find the slope of the line between each pair of points.

$\left(4 , −5\right) , \left(1 , −2\right)$

2.5

3.2 Exercise 68

Identify the slope and y-intercept of each line.

$y = −7 x + 3$

2.5

3.2 Exercise 70

Identify the slope and y-intercept of each line.

$3 x + y = 5$

2.5

3.2 Exercise 72

Identify the slope and y-intercept of each line.

$6 x + 4 y = 12$

2.5

3.2 Exercise 74

Identify the slope and y-intercept of each line.

$5 x - 2 y = 6$

2.5

3.2 Exercise 84

Determine the most convenient method to graph each line.

$x = 2$

2.5

3.2 Exercise 86

Determine the most convenient method to graph each line.

$y = −3 x + 4$

2.5

3.2 Exercise 88

Determine the most convenient method to graph each line.

$x - y = 1$

2.5

3.2 Exercise 90

Determine the most convenient method to graph each line.

$3 x - 2 y = −12$

2.5