Answer:
The x-intercept is [tex]x = -4[/tex]
The y-intercept is [tex]y = 2[/tex]
Step-by-step explanation:
A first order function has the following format:
[tex]y = ax + b[/tex]
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:
[tex]4(x - y) + 3 = 2x - 5[/tex]
[tex]4x - 4y + 3 = 2x - 5[/tex]
[tex]-4y = 2x - 5 - 4x - 3[/tex]
[tex]-4y = -2x - 8[/tex]
Multiplying by -1.
[tex]4y = 2x + 8[/tex]
[tex]y = \frac{2x + 8}{4}[/tex]
[tex]y = 0.5x + 2[/tex]
x-intercept
Value of x when y = 0.
[tex]y = 0.5x + 2[/tex]
[tex]0.5x + 2 = 0[/tex]
[tex]0.5x = -2[/tex]
[tex]x = -\frac{2}{0.5}[/tex]
[tex]x = -4[/tex]
The x-intercept is [tex]x = -4[/tex]
y-intercept
Value of y when x = 0.
[tex]y = 0.5x + 2[/tex]
[tex]y = 0.5(0) + 2[/tex]
[tex]y = 2[/tex]
The y-intercept is [tex]y = 2[/tex]
