Question

Select the table that represents a linear function. (Graph them if necessary.)

Answer 1

B

Explanation:

Answer 2

table B represents the linear equation which is:

`y=-3x+11`

The graph of the linear function is also attached below.

Explanation:

Given the table B values

x y

0 11

1 8

2 5

3 2

As the equation for the linear function

`y=mx+b`

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

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(0,\:11\right),\:\left(x_2,\:y_2\right)=\left(1,\:8\right)`

`m=(8-11)/(1-0)`

`m=-3`

so substituting the value m=-3 and the point (1, 8) in the point-slope form

`y-y_1=m\left(x-x_1\right)`

`y-8=-3\left(x-1\right)`

`y-8=-3x+3`

`y=-3x+3+8`

`y=-3x+11`

comparing the equation with the slope-intercept form of linear equation

`y=mx+b`

`y=-3x+11`

here

• m=slope=-3

• b=y-intercept=11

Therefore, table B represents the linear equation which is:

`y=-3x+11`

The graph of the linear function is also attached below.