Question

Find each x- and y-intercept.

4(x-y)+3=2x-5

Answer 1

The x-intercept is
`x = -4`

The y-intercept is
`y = 2`

Explanation:

A first order function has the following format:

`y = ax + b`

In which a is the slope and b is the y-intercept, that is, the value of y when x = 0. The x-intercept is the value of x when y = 0.

We have the following equation:

`4(x - y) + 3 = 2x - 5`

`4x - 4y + 3 = 2x - 5`

`-4y = 2x - 5 - 4x - 3`

`-4y = -2x - 8`

Multiplying by -1.

`4y = 2x + 8`

`y = (2x + 8)/(4)`

`y = 0.5x + 2`

x-intercept

Value of x when y = 0.

`y = 0.5x + 2`

`0.5x + 2 = 0`

`0.5x = -2`

`x = -(2)/(0.5)`

`x = -4`

The x-intercept is
`x = -4`

y-intercept

Value of y when x = 0.

`y = 0.5x + 2`

`y = 0.5(0) + 2`

`y = 2`

The y-intercept is
`y = 2`