Chapter 3.4, Problem 28PPS

To determine

To write an equation of line through $(0,5)$ and $(3,3)$ in slope intercept form.

Answer to Problem 28PPS

Slope intercept form

  $y=\frac{-2}{3}x+5$

Explanation of Solution

Given information:

Line through $(0,5)$ and $(3,3)$

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

$(0,5)$ and $(3,3)$

Here

  $x_1=0$

  $y_1=5$

  $x_2=3$

  $y_2=3$

Using slope formula to calculate slope of line

  $m=\frac{3-5}{3-0}$

On solving

  $m=\frac{-2}{3}$

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

  $m=\frac{-2}{3}$

Let take point $(0,5)$

Here

  $x_1=0$

  $y_1=5$

Point-slope form

  $y-5=\frac{-2}{3}(x-0)$

On solving

  $y-5=\frac{-2}{3}x$

Add 5 both sides

  $y-5+5=\frac{-2}{3}x+5$

On solving

  $y=\frac{-2}{3}x+5$

Hence, slope intercept form is $y=\frac{-2}{3}x+5$