Question

use the point - slope formula to write an equation of the line that passes through (0, 2) and (-5, 0). write the answer in slope - intercept form (if possible). the equation of the line is \square.

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$. Substitute $(x_1,y_1)=(0,2)$ and $(x_2,y_2)=(-3,0)$:
$m=\frac{0-2}{-3-0}=\frac{-2}{-3}=\frac{2}{3}$

Step2: Use point-slope form

Point-slope form is $y-y_1=m(x-x_1)$. Use $(x_1,y_1)=(0,2)$:
$y-2=\frac{2}{3}(x-0)$

Step3: Simplify to slope-intercept form

Slope-intercept form is $y=mx+b$. Simplify the equation:
$y-2=\frac{2}{3}x$
$y=\frac{2}{3}x+2$

Answer:

$y=\frac{2}{3}x+2$