Chapter 3.4, Problem 34PPS

To determine

To write an equation of line through $(-4,-5)$ and $(-8,-13)$ in slope intercept form.

Answer to Problem 34PPS

Slope intercept form

  $y=2x+3$

Explanation of Solution

Given information:

Line through $(-4,-5)$ and $(-8,-13)$

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

$(-4,-5)$ and $(-8,-13)$

Here

  $x_1=-4$

  $y_1=-5$

  $x_2=-8$

  $y_2=-13$

Using slope formula to calculate slope of line

  $m=\frac{-13-(-5)}{-8-(-4)}$

On solving

  $m=\frac{-8}{-4}$

On solving

  $m=2$

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

  $m=2$

Let take point $(-4,-5)$

Here

  $x_1=-4$

  $y_1=-5$

Point-slope form

  $y-(-5)=2(x-(-4))$

On solving

  $y+5=2(x+4)$

On solving

  $y+5=2x+8$

Subtract 5 both sides

  $y+5-5=2x+8-5$

On solving

  $y=2x+3$

Hence, slope intercept form is $y=2x+3$