Question

1. write the equation of the line going through points (10, 8) and (4, -4).

Explanation:

Step1: Calculate slope $m$

Use slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
Let $(x_1,y_1)=(10,8)$ and $(x_2,y_2)=(4,-4)$
$m=\frac{-4-8}{4-10}=\frac{-12}{-6}=2$

Step2: Find y-intercept $b$

Use point-slope form $y-y_1=m(x-x_1)$, substitute $m=2$, $(x_1,y_1)=(10,8)$
$y-8=2(x-10)$
Simplify: $y-8=2x-20$
Solve for $b$: $y=2x-20+8=2x-12$

Answer:

$y=2x-12$