Respuesta :
Answer:
The x-intercept is [tex](4,0)[/tex]
The y-intercept is [tex](0,-3)[/tex]
Step-by-step explanation:
Suppose you have a function f:
[tex]f = f(x,y) = 0[/tex]
The x-intercept is the value of x when [tex]y = 0[/tex].
The x-intercept is the value of y when [tex]x = 0[/tex].
Solution
We have:
[tex]f(x,y) = -3x + 4y = -12[/tex]
[tex]-3x + 4y + 12 = 0[/tex]
x-intercept
The x-intercept is the value of x when [tex]y = 0[/tex]. So:
[tex]-3x + 4(0) + 12 = 0[/tex]
[tex]-3x + 12 = 0[/tex]*(-1)
[tex]3x - 12 = 0[/tex]
[tex]3x = 12[/tex]
[tex]x = \frac{12}{3}[/tex]
[tex]x = 4[/tex]
The x-intercept is [tex](4,0)[/tex]
y-intercept
The y-intercept is the value of y when [tex]x = 0[/tex]. So:
[tex]-3(0) + 4y + 12 = 0[/tex]
[tex]4y + 12 = 0[/tex]
[tex]4y = -12[/tex]
[tex]y = \frac{-12}{4}[/tex]
[tex]y = -3[/tex]
The y-intercept is [tex](0,-3)[/tex]
