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

$-6x+8y=6 \\ \\ 8y=6x+6 \\ \\ y=\frac{3}{4}x+\frac{3}{4}$

The slope of the given line is 3/4.

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

$y-2=\frac{3}{4}(x+1)$

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

$y-2=-\frac{4}{3}(x+1)$