Answer:
Option A is correct.
Step-by-step explanation:
Given
To determine
What is the equation in the standard form of the line that passes through the point (4, −8) and has a slope of 1/4.
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where
substituting the values m = 1/4 and the point (4, -8)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-\left(-8\right)=\frac{1}{4}\left(x-4\right)[/tex]
[tex]y+8=\frac{1}{4}\left(x-4\right)[/tex]
Subtract 8 from both sides
[tex]y+8-8=\frac{1}{4}\left(x-4\right)-8[/tex]
[tex]y=\frac{1}{4}x-1-8[/tex]
[tex]y=\frac{1}{4}x-9[/tex]
Writing the equation in the standard form
As we know that the equation in the standard form is
Ax+By=C
where x and y are variables and A, B and C are constants
so
[tex]y=\frac{1}{4}x-9[/tex]
[tex]x=4y+36[/tex]
[tex]x - 4y = 36[/tex]
Therefore, the equation in the standard form of the line that passes through the point (4, −8) and has a slope of 1/4 will be:
[tex]x - 4y = 36[/tex]
Hence, option A is correct.
