write an equation in slope - intercept form for the graph shown.

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Find the y - intercept

The line crosses the y - axis at the point $(0, - 1)$, so $b=-1$.

Step3: Calculate the slope

The slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using the points $(0,-1)$ and $(2,-3)$, we have $m=\frac{-3-( - 1)}{2 - 0}=\frac{-3 + 1}{2}=\frac{-2}{2}=-1$.

Step4: Write the equation

Substitute $m=-1$ and $b = - 1$ into $y=mx + b$. We get $y=-x - 1$.

Answer:

$y=-x - 1$