determine the equation of the line shown in the graph below. enter your answer in slope-intercept form.

Explanation:

Step1: Identify slope from graph

The line rises 1 unit for every 2 units run, so slope $m=\frac{1}{2}$.

Step2: Use point to find intercept

Substitute $(x,y)=(4,1)$ and $m=\frac{1}{2}$ into $y=mx+b$: $1 = \frac{1}{2}(4) + b$ $1 = 2 + b$ Solve for $b$: $b=1-2=-1$

Step3: Write slope-intercept equation

Substitute $m=\frac{1}{2}$ and $b=-1$ into $y=mx+b$.

Answer:

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