Question

5.3 for use with pages 309-314
write an equation of the line shown. use the right-hand point to write
the equation.
19.
points: (-2, 3), (-5, -3)
20.
points: (4, 6), (-4, 0)
21.
points: (-1, -2), (1, -8)
22.
points: (1, 3), (-2, -2)
23.
points: (-3, 6), (3, 0)
24.
points: (0, 2), (5, -3)

Explanation:

Problem 19

Step1: Calculate slope $m$

$m=\frac{3-(-3)}{-2-(-5)}=\frac{6}{3}=2$

Step2: Use point-slope form

$y-3=2(x-(-2))$

Step3: Simplify to slope-intercept

$y=2x+4+3=2x+7$

Problem 20

Step1: Calculate slope $m$

$m=\frac{6-0}{4-(-4)}=\frac{6}{8}=\frac{3}{4}$

Step2: Use point-slope form

$y-6=\frac{3}{4}(x-4)$

Step3: Simplify to slope-intercept

$y=\frac{3}{4}x-3+6=\frac{3}{4}x+3$

Problem 21

Step1: Calculate slope $m$

$m=\frac{-8-(-2)}{1-(-1)}=\frac{-6}{2}=-3$

Step2: Use point-slope form

$y-(-8)=-3(x-1)$

Step3: Simplify to slope-intercept

$y=-3x+3-8=-3x-5$

Problem 22

Step1: Calculate slope $m$

$m=\frac{3-(-2)}{1-(-2)}=\frac{5}{3}$

Step2: Use point-slope form

$y-3=\frac{5}{3}(x-1)$

Step3: Simplify to slope-intercept

$y=\frac{5}{3}x-\frac{5}{3}+3=\frac{5}{3}x+\frac{4}{3}$

Problem 23

Step1: Calculate slope $m$

$m=\frac{0-6}{3-(-3)}=\frac{-6}{6}=-1$

Step2: Use point-slope form

$y-0=-1(x-3)$

Step3: Simplify to slope-intercept

$y=-x+3$

Problem 24

Step1: Calculate slope $m$

$m=\frac{-3-2}{5-0}=\frac{-5}{5}=-1$

Step2: Use point-slope form

$y-2=-1(x-0)$

Step3: Simplify to slope-intercept

$y=-x+2$

Answer:

1. $y=2x+7$
2. $y=\frac{3}{4}x+3$
3. $y=-3x-5$
4. $y=\frac{5}{3}x+\frac{4}{3}$
5. $y=-x+3$
6. $y=-x+2$