3.3 Find the Equation of a Line

Building an equation from a slope and a point, from two points, or from a parallel or perpendicular condition, using point-slope form as the hinge.

Intermediate Algebra 2e, 3.3 Find the Equation of a Line

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61 exercises

3.3 Exercise 1

Before you get started, take this readiness quiz.

Simplify: $\frac{2}{5} \left(x + 15\right) .$
If you missed this problem, review the reference.

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3.3 Exercise 2

Simplify: $−3 \left(x - \left(−2\right)\right) .$
If you missed this problem, review the reference.

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3.3 Exercise 3

Solve for y: $y - 3 = −2 \left(x + 1\right) .$
If you missed this problem, review the reference.

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3.3 Exercise 5

Find the equation of a line with slope $\frac{2}{5}$ and y-intercept $\left(0 , 4\right) .$

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3.3 Exercise 6

Find the equation of a line with slope $−1$ and y-intercept $\left(0 , −3\right) .$

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3.3 Exercise 11

Find the equation of a line with slope $m = - \frac{2}{5}$ and containing the point $\left(10 , −5\right) .$

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3.3 Exercise 12

Find the equation of a line with slope $m = - \frac{3}{4} ,$ and containing the point $\left(4 , −7\right) .$

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3.3 Exercise 14

Find the equation of a horizontal line containing the point $\left(−3 , 8\right) .$

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3.3 Exercise 15

Find the equation of a horizontal line containing the point $\left(−1 , 4\right) .$

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3.3 Exercise 17

Find the equation of a line containing the points $\left(−2 , −4\right)$ and $\left(1 , −3\right) .$

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3.3 Exercise 18

Find the equation of a line containing the points $\left(−4 , −3\right)$ and $\left(1 , −5\right) .$

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3.3 Exercise 19

Find an equation of a line that contains the points $\left(−3 , 5\right)$ and $\left(−3 , 4\right) .$ Write the equation in slope-intercept form.

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3.3 Exercise 20

Find the equation of a line containing the points $\left(5 , 1\right)$ and $\left(5 , −4\right) .$

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3.3 Exercise 21

Find the equation of a line containing the points $\left(−4 , 4\right)$ and $\left(−4 , 3\right) .$

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3.3 Exercise 23

Find an equation of a line parallel to the line $y = 3 x + 1$ that contains the point $\left(4 , 2\right) .$ Write the equation in slope-intercept form.

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3.3 Exercise 24

Find an equation of a line parallel to the line $y = \frac{1}{2} x - 3$ that contains the point $\left(6 , 4\right) .$

Write the equation in slope-intercept form.

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3.3 Exercise 26

Find an equation of a line perpendicular to the line $y = 3 x + 1$ that contains the point $\left(4 , 2\right) .$ Write the equation in slope-intercept form.

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3.3 Exercise 27

Find an equation of a line perpendicular to the line $y = \frac{1}{2} x - 3$ that contains the point $\left(6 , 4\right) .$ Write the equation in slope-intercept form.

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3.3 Exercise 28

Find an equation of a line perpendicular to $x = 5$ that contains the point $\left(3 , −2\right) .$ Write the equation in slope-intercept form.

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3.3 Exercise 29

Find an equation of a line that is perpendicular to the line $x = 4$ that contains the point $\left(4 , −5\right) .$ . Write the equation in slope-intercept form.

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3.3 Exercise 30

Find an equation of a line that is perpendicular to the line $x = 2$ that contains the point $\left(2 , −1\right) .$ Write the equation in slope-intercept form.

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3.3 Exercise 31

Find an equation of a line that is perpendicular to $y = −3$ that contains the point $\left(−3 , 5\right) .$ Write the equation in slope-intercept form.

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3.3 Exercise 32

Find an equation of a line that is perpendicular to the line $y = 1$ that contains the point $\left(−5 , 1\right) .$ Write the equation in slope-intercept form.

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3.3 Exercise 33

Find an equation of a line that is perpendicular to the line $y = −5$ that contains the point $\left(−4 , −5\right) .$ Write the equation in slope-intercept form.

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3.3 Exercise 34

Find the equation of a line with given slope and y-intercept. Write the equation in slope-intercept form.

slope 3 and
$y$ -intercept $\left(0 , 5\right)$

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3.3 Exercise 36

Find the equation of a line with given slope and y-intercept. Write the equation in slope-intercept form.

slope $−3$ and
$y$ -intercept $\left(0 , −1\right)$

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3.3 Exercise 38

Find the equation of a line with given slope and y-intercept. Write the equation in slope-intercept form.

slope $\frac{1}{5}$ and
$y$ -intercept $\left(0 , −5\right)$

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3.3 Exercise 40

Find the equation of a line with given slope and y-intercept. Write the equation in slope-intercept form.

slope 0 and
$y$ -intercept $\left(0 , −1\right)$

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3.3 Exercise 50

Find the equation of a line with given slope and containing the given point. Write the equation in slope-intercept form.

$m = \frac{5}{8} ,$ point $\left(8 , 3\right)$

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3.3 Exercise 52

Find the equation of a line with given slope and containing the given point. Write the equation in slope-intercept form.

$m = - \frac{3}{5} ,$ point $\left(10 , −5\right)$

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3.3 Exercise 54

Find the equation of a line with given slope and containing the given point. Write the equation in slope-intercept form.

$m = - \frac{3}{2} ,$ point $\left(−4 , −3\right)$

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3.3 Exercise 56

Find the equation of a line with given slope and containing the given point. Write the equation in slope-intercept form.

$m = −7 ,$ point $\left(−1 , −3\right)$

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3.3 Exercise 58

Find the equation of a line with given slope and containing the given point. Write the equation in slope-intercept form.

Horizontal line containing $\left(−2 , 5\right)$

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3.3 Exercise 60

Find the equation of a line with given slope and containing the given point. Write the equation in slope-intercept form.

Horizontal line containing $\left(−1 , −7\right)$

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3.3 Exercise 62

Find the equation of a line containing the given points. Write the equation in slope-intercept form.

$\left(2 , 6\right)$ and $\left(5 , 3\right)$

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3.3 Exercise 64

Find the equation of a line containing the given points. Write the equation in slope-intercept form.

$\left(−3 , −4\right)$ and $\left(5 , - 2\right)$

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3.3 Exercise 66

Find the equation of a line containing the given points. Write the equation in slope-intercept form.

$\left(−1 , 3\right)$ and $\left(−6 , −7\right)$

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3.3 Exercise 68

Find the equation of a line containing the given points. Write the equation in slope-intercept form.

$\left(0 , 4\right)$ and $\left(2 , −3\right)$

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3.3 Exercise 70

Find the equation of a line containing the given points. Write the equation in slope-intercept form.

$\left(7 , 2\right)$ and $\left(7 , −2\right)$

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3.3 Exercise 72

Find the equation of a line containing the given points. Write the equation in slope-intercept form.

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

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3.3 Exercise 74

Find an equation of a line parallel to the given line and contains the given point. Write the equation in slope-intercept form.

line $y = 4 x + 2 ,$
point $\left(1 , 2\right)$

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3.3 Exercise 76

Find an equation of a line parallel to the given line and contains the given point. Write the equation in slope-intercept form.

line $2 x - y = 6 ,$
point $\left(3 , 0\right) .$

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3.3 Exercise 78

Find an equation of a line parallel to the given line and contains the given point. Write the equation in slope-intercept form.

line $x = −4 ,$
point $\left(−3 , −5\right) .$

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3.3 Exercise 80

Find an equation of a line parallel to the given line and contains the given point. Write the equation in slope-intercept form.

line $y = 5 ,$
point $\left(2 , −2\right)$

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