Question

write an equation of the line that passes through the given points. use the first point to write the equation.

1. (9,4),(17,6)
2. (-3,10),(4,2)
3. (3,-8),(7,-2)
4. (-4,-4),(2,5)

Explanation:

Step1: Find slope for #25

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{6-4}{17-9}=\frac{2}{8}=\frac{1}{4}$

Step2: Point-slope form for #25

Use point $(9,4)$: $y-y_1=m(x-x_1)$
$y-4=\frac{1}{4}(x-9)$

Step3: Simplify to slope-intercept #25

$y=\frac{1}{4}x-\frac{9}{4}+4$
$y=\frac{1}{4}x+\frac{7}{4}$

Step1: Find slope for #26

$m=\frac{2-10}{4-(-3)}=\frac{-8}{7}$

Step2: Point-slope form for #26

Use point $(-3,10)$: $y-10=-\frac{8}{7}(x+3)$

Step3: Simplify to slope-intercept #26

$y=-\frac{8}{7}x-\frac{24}{7}+10$
$y=-\frac{8}{7}x+\frac{46}{7}$

Step1: Find slope for #27

$m=\frac{-2-(-8)}{7-3}=\frac{6}{4}=\frac{3}{2}$

Step2: Point-slope form for #27

Use point $(3,-8)$: $y+8=\frac{3}{2}(x-3)$

Step3: Simplify to slope-intercept #27

$y=\frac{3}{2}x-\frac{9}{2}-8$
$y=\frac{3}{2}x-\frac{25}{2}$

Step1: Find slope for #28

$m=\frac{5-(-4)}{2-(-4)}=\frac{9}{6}=\frac{3}{2}$

Step2: Point-slope form for #28

Use point $(-4,-4)$: $y+4=\frac{3}{2}(x+4)$

Step3: Simplify to slope-intercept #28

$y=\frac{3}{2}x+6-4$
$y=\frac{3}{2}x+2$

Answer:

1. $y=\frac{1}{4}x+\frac{7}{4}$
2. $y=-\frac{8}{7}x+\frac{46}{7}$
3. $y=\frac{3}{2}x-\frac{25}{2}$
4. $y=\frac{3}{2}x+2$