Question

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

Explanation:

Step1: Recall slope-intercept form

Slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

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

The line crosses the y - axis at $(0,-5)$, so $b=-5$.

Step3: Calculate the slope ($m$)

The formula for slope between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. We have two points: $(0,-5)$ (let $x_1 = 0,y_1=-5$) and $(4,-2)$ (let $x_2 = 4,y_2=-2$).
Substitute into the slope formula: $m=\frac{-2-(-5)}{4 - 0}=\frac{-2 + 5}{4}=\frac{3}{4}$.

Step4: Write the equation

Substitute $m=\frac{3}{4}$ and $b = - 5$ into $y=mx + b$.
We get $y=\frac{3}{4}x-5$.

Answer:

$y=\frac{3}{4}x - 5$