Question

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

Explanation:

Step1: Identify coordinate pairs

From the graph:
$(x_1,y_1)=(3,0)$, $(x_2,y_2)=(4,1)$, $(x_3,y_3)=(5,2)$,...,$(x_n,y_n)=(19,16)$

Step2: Calculate slope $m$

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{1-0}{4-3}=1$

Step3: Find y-intercept $b$

Use $y=mx+b$, substitute $(3,0)$ and $m=1$:
$0=1\times3+b$
$b=0-3=-3$

Step4: Write the equation

Substitute $m=1$ and $b=-3$ into $y=mx+b$
$y=x-3$

Step5: Complete the table (sample pairs)

For any $x$, $y=x-3$:
When $x=3$, $y=0$; $x=4$, $y=1$; $x=5$, $y=2$; $x=6$, $y=3$; $x=7$, $y=4$; $x=8$, $y=5$; $x=9$, $y=6$; $x=10$, $y=7$; $x=11$, $y=8$; $x=12$, $y=9$; $x=13$, $y=10$; $x=14$, $y=11$; $x=15$, $y=12$; $x=16$, $y=13$; $x=17$, $y=14$; $x=18$, $y=15$; $x=19$, $y=16$

Answer:

Completed Table (selected pairs):

$x$	$y$
4	1
5	2
6	3
7	4
8	5
9	6
10	7
11	8
12	9
13	10
14	11
15	12
16	13
17	14
18	15
19	16

Equation:

$y = x - 3$