Question

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

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $(0, 3)$, so $b=3$.

Step2: Calculate slope using two points

Use points $(0,3)$ and $(1,-1)$. Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{-1-3}{1-0}=\frac{-4}{1}=-4$

Step3: Substitute into slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m=-4$ and $b=3$.

Answer:

$y=-4x+3$