write an equation for this line in slope - intercept form.

Explanation:

Step1: Find the slope ($m$)

Use the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points on the line, say $(0,3)$ (y - intercept, so $x_1 = 0,y_1=3$) and $(1, - 1)$ ($x_2 = 1,y_2=-1$). $m=\frac{-1 - 3}{1 - 0}=\frac{-4}{1}=-4$

Step2: Identify the y - intercept ($b$)

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

Step3: Write the equation in slope - intercept form ($y=mx + b$)

Substitute $m=-4$ and $b = 3$ into the formula. $y=-4x + 3$

Answer:

$y=-4x + 3$