Question

Write the linear equation that gives the rule for this table.

x f(x)
0 0
1 9
2 18
3 27

Answer 1

`f(x) = 9x`

Explanation:

Given

The attached table

Required

Rule of the table

First, we calculate the slope(m)

`m = (y_2 -y_1)/(x_2 - x_1)`

Where

`(x_1,y_1) = (0,0)`

`(x_2,y_2) = (3,27)`

`m = (27 -0)/(3 - 0)`

`m = (27)/(3)`

`m = 9`

The table equation is:

`y - y_1 = m(x - x_1)`

So, we have:

`y - 0 = 9(x - 0)`

`y - 0 = 9(x)`

`y= 9x`

Hence:

`f(x) = 9x`