Question

complete the table and write the equation for the relationship shown in the graph.

Explanation:

Step1: Extract points from graph

Identify coordinates: $(0,0), (3,1), (6,2), (9,3), (12,4), (15,5), (18,6)$

Step2: Find slope $m$

Calculate ratio of $\Delta y$ to $\Delta x$.
$m=\frac{1-0}{3-0}=\frac{1}{3}$

Step3: Determine y-intercept $b$

Line passes through $(0,0)$, so $b=0$.

Step4: Write linear equation

Use slope-intercept form $y=mx+b$.
$y=\frac{1}{3}x$

Step5: Verify with other points

Check $(18,6)$: $y=\frac{1}{3}(18)=6$, which matches.

Answer:

Completed Table (x, y):

(0, 0), (3, 1), (6, 2), (9, 3), (12, 4), (15, 5), (18, 6)

Equation:

$y=\frac{1}{3}x$