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

Explanation:

Step1: Recall slope-intercept form

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

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

From the graph, the line crosses the y - axis at the point $(0,-2)$. In the slope - intercept form $y=mx + b$, when $x = 0$, $y=b$. So, $b=-2$.

Step3: Calculate the slope ($m$)

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. We have two points on the line: $(0,-2)$ and $(1,0)$. Let $(x_1,y_1)=(0,-2)$ and $(x_2,y_2)=(1,0)$. Then $m=\frac{0-(-2)}{1 - 0}=\frac{0 + 2}{1}=2$.

Step4: Write the equation

Substitute $m = 2$ and $b=-2$ into the slope - intercept form $y=mx + b$. We get $y=2x-2$.

Answer:

$y = 2x-2$