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 on the line

Choose $(x_1,y_1)=(6,0)$ and $(x_2,y_2)=(10,4)$.

Step3: Calculate the slope

$m=\frac{4-0}{10-6}=\frac{4}{4}=1$

Step4: Find y-intercept $b$

Use slope-intercept form $y=mx+b$, substitute $m=1$ and $(6,0)$:
$0=1\times6+b$
Solve for $b$: $b=0-6=-6$

Step5: Write the equation

Substitute $m=1$ and $b=-6$ into $y=mx+b$.

Answer:

$y=x-6$