Question

Writing equations of lines parallel and perpendicular to a given...

Consider the line −6x+8y=6.
Find the equation of the line that is perpendicular to this line and passes through the point (-1, 2).
Find the equation of the line that is parallel to this line and passes through the point (-1, 2)

Answer 1

`-6x+8y=6 \\ \\ 8y=6x+6 \\ \\ y=(3)/(4)x+(3)/(4)`

The slope of the given line is 3/4.

Parallel lines have the same slope, so the equation is:

`y-2=(3)/(4)(x+1)`

Perpendicular lines have slopes that are negative reciprocals, so the equation is:

`y-2=-(4)/(3)(x+1)`