Question

Select the equation that represents the graph of the line y=x-1 y=1/2x-1 y=1/2x + 2 y=x+2​

Answer 1

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

Explanation:

Given

See attachment for graph

Required

The graph equation

First, pick any two corresponding points on the line

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

`(x_2,y_2) = (4,1)`

Calculate slope (m)

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

This gives:

`m = (1 - 0)/(4 - 2)`

`m = (1)/(2)`

The line equation is then calculated as:

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

Where

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

`m = (1)/(2)`

So:

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

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

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

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