Question

write the equation of the line in fully simplified slope - intercept form.

Explanation:

Step1: Identify intercept and point

The y-intercept $b=5$ (where line crosses y-axis). A point on the line is $(3, -7)$.

Step2: Calculate slope $m$

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$.
$m=\frac{-7 - 5}{3 - 0}=\frac{-12}{3}=-4$

Step3: Write slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m=-4$ and $b=5$.
$y=-4x+5$

Answer:

$y=-4x+5$