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 line

Choose $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(5,5)$.

Step3: Calculate the slope

$m=\frac{5-0}{5-0}=1$

Step4: Find y-intercept

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

Step5: Write linear equation

Use $y=mx+b$, substitute $m=1$ and $b=0$.

Answer:

$y=x$