Answer:
x-intercept = 10
y-intercept = -8
Step-by-step explanation:
[tex]4x-5y=40[/tex]
To identify the y-intercept, we will need to format the equation in the form [tex]y=mx+b[/tex]. We can start by subtracting [tex]4x[/tex] from both sides of the equation:
[tex]-5y=-4x+40[/tex]
Divide both sides of the equation by the coefficient of [tex]y[/tex], which is [tex]-5[/tex]:
[tex]y=\frac{-4}{-5} x - 8[/tex]
The [tex]b[/tex] is representative of the y-intercept in [tex]y=mx+b[/tex].
Identify [tex]b[/tex] in the equation [tex]y=\frac{-4}{-5} x - 8[/tex]:
[tex]b=-8[/tex]
Therefore, our y-intercept is -8.
To solve for the x-intercept, replace the [tex]y[/tex] in the equation [tex]y=\frac{-4}{-5} x - 8[/tex] with a zero:
[tex]0=\frac{-4}{-5} x - 8[/tex]
Add [tex]8[/tex] to both sides of the equation:
[tex]8=\frac{-4}{-5} x[/tex]
You can go ahead and divide [tex]-4[/tex] by [tex]-5[/tex] to get rid of the fraction:
[tex]8=0.8x[/tex]
Divide both sides of the equation by the coefficient of [tex]x[/tex], which is [tex]0.8[/tex]:
[tex]10=x[/tex]
Therefore, our x-intercept is 10.
