a line passes through the points (-3, 2) and (5, -4). write its equation in slope - intercept form. write…

Answer:

$y = -\frac{3}{4}x+\frac{5}{4}$

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Given $(x_1,y_1)=(-3,2)$ and $(x_2,y_2)=(5,-4)$, then $m=\frac{-4 - 2}{5-(-3)}=\frac{-6}{8}=-\frac{3}{4}$.

Step2: Find the y - intercept

Use the point - slope form $y - y_1=m(x - x_1)$ with the point $(-3,2)$ and $m = -\frac{3}{4}$. So $y - 2=-\frac{3}{4}(x+3)$. Expand it: $y-2=-\frac{3}{4}x-\frac{9}{4}$. Add 2 to both sides: $y=-\frac{3}{4}x-\frac{9}{4}+2$. Since $2=\frac{8}{4}$, then $y = -\frac{3}{4}x+\frac{-9 + 8}{4}=-\frac{3}{4}x+\frac{5}{4}$.