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

Step3: Plug into slope-intercept form

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

Answer:

$y=4x-3$