Chapter 3.4, Problem 31PPS

To determine

To write an equation of line in slope intercept form.

Answer to Problem 31PPS

Slope intercept form

  $y=-10x+26$

Explanation of Solution

Given information:

Graph

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:

On considering graph Point $E(2,6)$ and $F(3,-4)$

Here

  $x_1=2$

  $y_1=6$

  $x_2=3$

  $y_2=-4$

Using slope formula to calculate slope of line

  $m=\frac{-4-6}{3-2}$

On solving

  $m=\frac{-10}{1}$

On solving

  $m=-10$

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

  $m=-10$

Let take point $E(2,6)$

Here

  $x_1=2$

  $y_1=6$

Point-slope form

  $y-6=-10(x-2)$

On solving

  $y-6=-10x+20$

Add 6 both sides

  $y-6+6=-10x+20+6$

On solving

  $y=-10x+26$

Hence, slope intercept form is $y=-10x+26$