Answer:
table B represents the linear equation which is:
[tex]y=-3x+11[/tex]
The graph of the linear function is also attached below.
Step-by-step explanation:
Given the table B values
x y
0 11
1 8
2 5
3 2
As the equation for the linear function
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept
As the y-intercept can be obtained by setting x=0
From the table, it is clear that when the value of x=0, then the value of
y=11.
so (0, 11) is the y-intercept.
Also taking two points (0, 11) and (1, 8) to find the slope
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(0,\:11\right),\:\left(x_2,\:y_2\right)=\left(1,\:8\right)[/tex]
[tex]m=\frac{8-11}{1-0}[/tex]
[tex]m=-3[/tex]
so substituting the value m=-3 and the point (1, 8) in the point-slope form
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-8=-3\left(x-1\right)[/tex]
[tex]y-8=-3x+3[/tex]
[tex]y=-3x+3+8[/tex]
[tex]y=-3x+11[/tex]
comparing the equation with the slope-intercept form of linear equation
[tex]y=mx+b[/tex]
[tex]y=-3x+11[/tex]
here
Therefore, table B represents the linear equation which is:
[tex]y=-3x+11[/tex]
The graph of the linear function is also attached below.
