Question

Which equation matches the graph of the greatest integer function given
below?

Answer 1

`y = x + 2`

Explanation:

Given

The attached graph

Required

Determine the equation

First, pick any 2 corresponding coordinates

`(x_1,y_1) = (0,2)`

`(x_2,y_2) = (6,8)`

Next, calculate the slope (m)

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

`m = (8-2)/(6-0)`

`m = (6)/(6)`

`m =1`

The equation is calculated as:

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

Where:

`(x_1,y_1) = (0,2)` and
`m =1`

`y - 2 = 1(x - 0)`

`y - 2 = (x - 0)`

`y - 2 = x`

Make y the subject

`y = x + 2`