Question

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

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $x=0$, $y=2$. So the y-intercept $b=2$.

Step2: Calculate slope

Pick two points, e.g., $(0,2)$ and $(8,10)$.
Slope $m=\frac{y_2-y_1}{x_2-x_1}=\frac{10-2}{8-0}=\frac{8}{8}=1$.

Step3: Write linear equation

Use slope-intercept form $y=mx+b$.
Substitute $m=1$, $b=2$: $y=x+2$.

Step4: Complete sample table

Use $y=x+2$ to find values:

• If $x=1$, $y=1+2=3$
• If $x=4$, $y=4+2=6$
• If $x=12$, $y=12+2=14$
• If $x=16$, $y=16+2=18$

Answer:

Completed Table (example pairs):

$x$	$y$
1	3
4	6
8	10
12	14
16	18

Equation:

$y=x+2$