Determine whether the graphs of any of the following equations are parallel or perpendicular. Explain.

Question

1. y=2/3x+3, y=3/2x, 2x-3y=8

1. y=4x, x+4y=12, 4x+y=1

Answer 1

1. 2x-3y=8 is the same as y=(2/3)x -8/3 which has slope = 2/3 making it parallel to y=2/3x+3. the other line y=(3/2)x is neither parallel or perpendicular, although it would be perpendicular if you add a minus sign to the 3/2. y=-(3/2)x
2. y=4x and x+4y=12 are perpendicular. 1st has slope = 4, 2nd has slope=-1/4, the negative inverse of 4. the 3rd is neither parallel or perpendicular as its slope is -4, change the sign though and it would be parallel to the 1st equation

Just rewrite them, so they're all in the form y=mx+b. If they have the same m, they're parallel. If they have slopes that are negative inverses, m and -1/m, then they're perpendicular