Question

Are the lines for the pair of equations parallel, perpendicular, or neither.

y = –2/3x + 1
2x – 3y = –3

Answer 1

the slope of the first line is \(-\frac{2}{3}\)
to find the slope of the second line write
\[2x-3y=-3\]
\[-3y=-2x-3\]
\[y=\frac{2}{3}x+1\] so it has slope \(\frac{2}{3}\)
the slopes are not the same, so they are not parallel
since \(\frac{2}{3}|\) is not the negative reciprocal of \(-\frac{2}{3}\) they are not perpendicular

Answer 2

Thanks! So if i had a diffrent problem and the slopes were the same it would be parallel?