Question

write in slope-intercept form the equation of the line that passes through the given points.

1. $(-3, 2), (4, -1)$
2. $(6, 2), (8, -4)$
3. $(-2, 5), (2, 4)$

Explanation:

Step1: Calculate slope for #13

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{-1-2}{4-(-3)}=\frac{-3}{7}$

Step2: Find y-intercept for #13

Use point $(-3,2)$: $2=\frac{-3}{7}(-3)+b$
$2=\frac{9}{7}+b$ → $b=2-\frac{9}{7}=\frac{14}{7}-\frac{9}{7}=\frac{5}{7}$

Step3: Write equation for #13

Slope-intercept form: $y=mx+b$
$y=-\frac{3}{7}x+\frac{5}{7}$
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Step1: Calculate slope for #14

$m=\frac{-4-2}{8-6}=\frac{-6}{2}=-3$

Step2: Find y-intercept for #14

Use point $(6,2)$: $2=-3(6)+b$
$2=-18+b$ → $b=2+18=20$

Step3: Write equation for #14

$y=-3x+20$
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Step1: Calculate slope for #15

$m=\frac{4-5}{2-(-2)}=\frac{-1}{4}$

Step2: Find y-intercept for #15

Use point $(-2,5)$: $5=\frac{-1}{4}(-2)+b$
$5=\frac{1}{2}+b$ → $b=5-\frac{1}{2}=\frac{10}{2}-\frac{1}{2}=\frac{9}{2}$

Step3: Write equation for #15

$y=-\frac{1}{4}x+\frac{9}{2}$

Answer:

1. $y=-\frac{3}{7}x+\frac{5}{7}$
2. $y=-3x+20$
3. $y=-\frac{1}{4}x+\frac{9}{2}$