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

Explanation:

Step1: Identify two - points

Choose two points on the line, say $(0,1)$ and $(2,2)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $(x_1,y_1)=(0,1)$ and $(x_2,y_2)=(2,2)$ gives $m=\frac{2 - 1}{2 - 0}=\frac{1}{2}$.

Step3: Identify the y - intercept $b$

The y - intercept is the y - value when $x = 0$. From the point $(0,1)$, $b = 1$.

Step4: Write the equation

The slope - intercept form is $y=mx + b$. Substituting $m=\frac{1}{2}$ and $b = 1$ gives $y=\frac{1}{2}x+1$.

Answer:

$y=\frac{1}{2}x + 1$