Question

What is an equation of the line that passes through the point (4, —4) and is parallel to the line 3x - 4y = 16?

Answer 1

`y = (3)/(4)x -7`

Explanation:

Linear Equations

They are typically written in slope-intercept form.

`y=mx+b` where m is the slope and b is the y-intercept

Parallel lines have equal slopes.

1. Rearrange the equation

`3x - 4y = 16\\- 4y = -3x +16\\\\y = (3)/(4)x -4`

2. Determine the equation

Since slopes are equal for parallel lines, we just have to determine the y-intercept of this new line.

`y = (3)/(4)x +b`

Plug in the given point:

`-4= (3)/(4)(4) +b\\\\-4= 3 +b\\b=-7`

Therefore:

`y = (3)/(4)x -7`