Question

1. write the equation of a line in slope intercept form give that the line passes through (-4,8) and (-7,-3).

Explanation:

Step1: Verify slope calculation

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{-3-8}{-7-(-4)}=\frac{-11}{-3}=\frac{11}{3}$

Step2: Use point-slope form

$y-y_1=m(x-x_1)$
Substitute $m=\frac{11}{3}$, $x_1=-4$, $y_1=8$:
$y-8=\frac{11}{3}(x-(-4))$

Step3: Simplify to slope-intercept

Expand right-hand side:
$y-8=\frac{11}{3}x+\frac{44}{3}$
Add 8 (or $\frac{24}{3}$) to both sides:
$y=\frac{11}{3}x+\frac{44}{3}+\frac{24}{3}=\frac{11}{3}x+\frac{68}{3}$

Answer:

$y=\frac{11}{3}x+\frac{68}{3}$