Question

Find each x- and y-intercept. 4(x-y)+3=2x-5

Answer 1

Answer:

The x-intercept is $x = -4$

The y-intercept is $y = 2$

Step-by-step 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.

$4y = 2x + 8$

$y = \frac{2x + 8}{4}$

$y = 0.5x + 2$

x-intercept

Value of x when y = 0.

$y = 0.5x + 2$

$0.5x + 2 = 0$

$0.5x = -2$

$x = -\frac{2}{0.5}$

$x = -4$

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 $y = 2$