Question

Write the equation of the line that goes through the point (−9, −4) and is parallel to the line −x + 3y = −0.5

Answer 1

`y = (1)/(3)x -1`

Step-by-step explanation:

Given

Parallel to:
`-x + 3y = -0.5`

Passes through (-9,-4)

Required

Determine the line equation

First, we calculate the slope (m) of the said line

`-x + 3y = -0.5`

Make y the subject

`3y = x - 0.5`

Divide through by 3

`y = (1)/(3)x - (0.5)/(3)`

An equation has the general form:

`y = mx + b`

Where

`m = slope`

So:

`m = (1)/(3)`

Because the required line is parallel to
`-x + 3y = -0.5`, then they have the same slope of
`m = (1)/(3)`

Next, is to calculate the line equation using:

`y = m(x - x_1) + y_1`

Where

`m = (1)/(3)`

`(x_1,y_1) = (-9,-4)`

This gives:

`y = (1)/(3)(x -(-9)) + (-4)`

`y = (1)/(3)(x +9) -4`

Open bracket

`y = (1)/(3)x +3 -4`

`y = (1)/(3)x -1`