Question

write the equation for the relationship shown in the graph.

Explanation:

Step1: Identify slope formula

The slope $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$.

Step2: Pick two points and calculate slope

Use points $(0,2)$ and $(1,3)$:
$m=\frac{3-2}{1-0}=1$

Step3: Find y-intercept $b$

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

Step4: Write slope-intercept equation

The slope-intercept form is $y=mx+b$. Substitute $m=1$ and $b=2$.
$y=1x+2$ or $y=x+2$

Answer:

$y=x+2$