Question

write the equation for the relationship shown in the graph.

Explanation:

Step1: Identify line form

We use slope-intercept form $y=mx+b$, where $m$ is slope, $b$ is y-intercept.

Step2: Find y-intercept

The line crosses the y-axis at $x=0$, but from the graph, when $x=10$, $y=0$. We use two points: $(10,0)$ and $(14,4)$.

Step3: Calculate slope

Slope $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{4-0}{14-10}=\frac{4}{4}=1$

Step4: Solve for b

Substitute $m=1$, $x=10$, $y=0$ into $y=mx+b$:
$0=1(10)+b$
$b=0-10=-10$

Step5: Write final equation

Substitute $m=1$, $b=-10$ into $y=mx+b$.

Answer:

$y=x-10$