Question

Given the equation of the line, 2x-3y=7, find each of the following:
a) an equation of the line through (2,-3) parallel to the given line.
b) an equation of the line through (-3,2) perpendicular to the given line.

Answer 1

(a) First, I would express the equation given in this form y=mx+n,
\[y=\frac{2}{3}x-\frac{7}{3}\]As the equation must be parallel, then
\[y=\frac{2}{3}x+n\] And now you force it to pass by (2,-3)
\[-3=\frac{4}{3}+n\Rightarrow n=-13/3\]
(b) For the second problem, follow the same path, but now the equation of the perpendicular will be y=-x/m+n, so,
\[y=-\frac{3}{2}x+n\]And force it to pass by (-3,2),
\[2=-9/2+n\Rightarrow n=13/2\]

Answer 2

now did you get the n?

Answer 3

@John_ES

Answer 4

The n in the first case was -13/3, and in the second 13/2, if I'm not mistaken.

Answer 5

ohhhh i see how you got it :) thanks!!! @John_ES