Question

Which equation represents the linear function that is shown on the graph below?

10.14
9
8
00
7 6 5
4 +
3
2
1
1 2 3 4 5 6 7 8 9
Х

Answer 1

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

Explanation:

Given

The attached graph

Required

Determine the linear equation

First, we need to calculate the slope

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

From the graph, the following relationships exist:

`(x_1,y_1) = (4,0)`

`(x_2,y_2) = (10,3)`

So, the expression for calculating slope becomes:

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

`m = (3-0)/(10-4)`

`m = (3)/(6)`

`m = (1)/(2)`

Next, we calculate the equation using:

`y - y_2 = m(x - x_2)`

This gives:

`y - 3 = (1)/(2)(x - 10)`

Open bracket

`y - 3 = (1)/(2)x - 5`

Make y the subject:

`y = (1)/(2)x - 5+3`

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