Question

.

Answer 1

Answer:

Option A is correct.

Step-by-step explanation:

Given

• The point (4, -8)

• Slope m = 1/4

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

$y-y_1=m\left(x-x_1\right)$

where

• m is the slope of the line

• (x₁, y₁) is the point

substituting the values m = 1/4 and the point (4, -8)

$y-y_1=m\left(x-x_1\right)$

$y-\left(-8\right)=\frac{1}{4}\left(x-4\right)$

$y+8=\frac{1}{4}\left(x-4\right)$

Subtract 8 from both sides

$y+8-8=\frac{1}{4}\left(x-4\right)-8$

$y=\frac{1}{4}x-1-8$

$y=\frac{1}{4}x-9$

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

$y=\frac{1}{4}x-9$

$x=4y+36$

$x - 4y = 36$

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:

$x - 4y = 36$

Hence, option A is correct.