Question

.

What is the equation in standard form of the line that passes through the point (4, −8) and has a slope of 1/4?

A) x − 4y = 36
B) x − 4y = −28
C) x − 4y = −36
D) x − 4y = 28

Answer 1

Option A is correct.

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)=(1)/(4)\left(x-4\right)`

`y+8=(1)/(4)\left(x-4\right)`

Subtract 8 from both sides

`y+8-8=(1)/(4)\left(x-4\right)-8`

`y=(1)/(4)x-1-8`

`y=(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=(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.