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

Explanation:

Step1: Find two points on the line

Let's take the points $(0, 2)$ and $(1,5)$.

Step2: Calculate the slope

The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{5 - 2}{1-0}=3$.

Step3: Use the slope - intercept form

The slope - intercept form is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. Since the line passes through $(0,2)$, $b = 2$. So the equation is $y=3x+2$.

Answer:

$y = 3x+2$