Question

find a formula for the linear function depicted in the following graph.

Explanation:

Step1: Identify two points on line

From the graph, the line passes through $(5, 0)$ and $(0, -2)$.

Step2: Calculate the slope

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$.
$m=\frac{0 - (-2)}{5 - 0}=\frac{2}{5}$

Step3: Find y-intercept

The line crosses the y-axis at $(0, -2)$, so $b=-2$.

Step4: Write linear function

Substitute $m$ and $b$ into $y=mx+b$.
$y=\frac{2}{5}x - 2$

Answer:

$y=\frac{2}{5}x - 2$