Question

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

Explanation:

Step1: Extract points from the graph

Identify coordinate pairs: $(9,0)$, $(10,1)$, $(11,2)$, $(12,3)$, $(13,4)$, $(14,5)$, $(15,6)$, $(16,7)$, $(17,8)$, $(18,9)$, $(19,10)$, $(20,12)$

Step2: Find slope ($m$)

Use two points to calculate slope.
$m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-0}{10-9}=1$

Step3: Find y-intercept ($b$)

Use $y=mx+b$, substitute $m=1$ and $(9,0)$:
$0=1\times9+b$
$b=0-9=-9$

Step4: Form the equation

Substitute $m=1$ and $b=-9$ into $y=mx+b$.
$y=x-9$

Step5: Verify with other points

Check $(15,6)$: $6=15-9=6$, which is correct.

Answer:

Completed Table (sample key points):

$x$	$y$
10	1
12	3
15	6
18	9
20	11

Equation:

$y = x - 9$