a line passes through the points (-4, -19) and (12, -7). write its equation in slope - intercept form. write…

Answer:

$y=\frac{3}{4}x - 16$

Explanation:

Step1: Calculate the slope

$m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-7-(-19)}{12 - (-4)}=\frac{-7 + 19}{12 + 4}=\frac{12}{16}=\frac{3}{4}$

Step2: Use point - slope form

$y - y_1=m(x - x_1)$, using the point $(12,-7)$ and $m = \frac{3}{4}$, we have $y+7=\frac{3}{4}(x - 12)$

Step3: Convert to slope - intercept form

$y+7=\frac{3}{4}x-9$, then $y=\frac{3}{4}x - 16$