Chapter 3.4, Problem 29PPS

To determine

To write an equation of line through $(-12,-6)$ and $(8,9)$ in slope intercept form.

Answer to Problem 29PPS

Slope intercept form

  $y=\frac{3}{4}x+3$

Explanation of Solution

Given information:

Line through $(-12,-6)$ and $(8,9)$

Formula used:

Slope, $m=\frac{y_2-y_1}{x_2-x_1}$

Point-slope form

  $y-y_1=m(x-x_1)$

Slope intercept form

  $y=mx+b$

Calculation:

Points

$(-12,-6)$ and $(8,9)$

Here

  $x_1=-12$

  $y_1=-6$

  $x_2=8$

  $y_2=9$

Using slope formula to calculate slope of line

  $m=\frac{9-(-6)}{8-(-12)}$

On solving

  $m=\frac{15}{20}$

On solving

  $m=\frac{3}{4}$

Using slope and any one of the point to find slope intercept form

  $m=\frac{3}{4}$

Let take point $(-12,-6)$

Here

  $x_1=-12$

  $y_1=-6$

Point-slope form

  $y-(-6)=\frac{3}{4}(x-(-12))$

On solving

  $y+6=\frac{3}{4}(x+12)$

On solving

  $y+6=\frac{3}{4}x+9$

Subtract 6 both sides

  $y+6-6=\frac{3}{4}x+9-6$

On solving

  $y=\frac{3}{4}x+3$

Hence, slope intercept form is $y=\frac{3}{4}x+3$