Chapter 3.4, Problem 35PPS

To determine

To write an equation of line whose x- intercept is 3 and y -intercept is $-2$ in slope intercept form.

Answer to Problem 35PPS

Slope intercept form

  $y=\frac{2}{3}x-2$

Explanation of Solution

Given information:

x- intercept of line is 3

And y -intercept of line is $-2$

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:

x- intercept of line $=3$

y -intercept of line is $=-2$

Here

x- intercept means y-coordinate will be zero

y -intercept means x -coordinate will be zero

Then rewrite x and y intercept in coordinate form

x- intercept of line $=(3,0)$

y -intercept of line is $=(0,-2)$

Here

  $x_1=3$

  $y_1=0$

  $x_2=0$

  $y_2=-2$

Using slope formula to calculate slope of line

  $m=\frac{-2-0}{0-3}$

On solving

  $m=\frac{-2}{-3}$

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 $(3,0)$

Here

  $x_1=3$

  $y_1=0$

Point-slope form

  $y-0=\frac{2}{3}(x-3)$

On solving

  $y=\frac{2}{3}x-2$

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