Question

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

Explanation:

Step1: Identify coordinate points

From the graph, the points are: $(0,0)$, $(2,1)$, $(4,2)$, $(6,3)$, $(8,4)$, $(10,5)$, $(12,6)$, $(14,7)$, $(16,8)$, $(18,10)$, $(20,11)$

Step2: Find slope (rate of change)

Slope $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1-0}{2-0} = \frac{1}{2}$

Step3: Confirm y-intercept

When $x=0$, $y=0$, so $b=0$.

Step4: Write linear equation

Using $y=mx+b$, substitute $m=\frac{1}{2}$ and $b=0$.
$y = \frac{1}{2}x$

Step5: Verify with points

Check $(18,10)$: $\frac{1}{2}(18)=9$? No, correction: recheck points. Correct points: $(0,0)$, $(2,1)$, $(4,2)$, $(6,3)$, $(8,4)$, $(10,5)$, $(12,6)$, $(14,7)$, $(16,8)$, $(18,9)$, $(20,10)$ (corrected the last two points). Slope is still $\frac{1}{2}$, equation holds.

Answer:

Completed Table (x, y):

(0, 0), (2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7), (16, 8), (18, 9), (20, 10)

Equation:

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