Question

Find the equation of the linear function represented by the table below in slope-intercept form.

x y

-2 -9

1 3

4 15

7 27

Answer 1

`y = 4x-1`

Explanation:

Required:

Determine the equation of the linear function

First, we need to determine the slope (m) as follows:

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

Where

`(x_1,y_1) = (-2,-9)`

`(x_2,y_2) = (4,15)`

Substitute these values in
`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (15- (-9))/(4 - (-2))`

`m = (24)/(6)`

`m =4`

The equation is then calculated using:

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

This gives:

`y -(-9) = 4(x - (-2))`

`y + 9 = 4(x + 2)`

`y + 9 = 4x + 8`

Make y the subject

`y = 4x + 8 - 9`

`y = 4x-1`