Question

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

Explanation:

Step1: Identify plotted points

The points from the graph are:
$(1,0)$, $(2,1)$, $(3,2)$, $(4,3)$, $(5,4)$, $(6,5)$, $(7,6)$, $(8,7)$, $(9,8)$, $(10,9)$, $(11,10)$

Step2: Find slope ($m$)

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

Step3: Find y-intercept ($b$)

Use $y=mx+b$, substitute $m=1$, $(x,y)=(1,0)$:
$0 = 1(1) + b$
$b = 0 - 1 = -1$

Step4: Write linear equation

Substitute $m=1$, $b=-1$ into $y=mx+b$:
$y = x - 1$

Step5: Build the table

Map $x$ values to $y=x-1$:

$x$	$y$
2	1
3	2
4	3
5	4
6	5
7	6
8	7
9	8
10	9
11	10

Answer:

Completed Table:

$x$	$y$
2	1
3	2
4	3
5	4
6	5
7	6
8	7
9	8
10	9
11	10

Equation:

$y = x - 1$