Question

Which equation represents a line that is perpendicular to the line represented by

y=2/3x+1?

1) 3x+2y=12

2) 3x-2y=12

3) y=3/2x+2

4) y= -2/3x+4

Answer 1

Answer: (1)

Explanation:

Perpendicular lines have slopes that are negative reciprocals. So, since the slope of the given line is 2/3, the slope of the line we want to find is -3/2.

Rearranging equations 1 and 2 into slope intercept form,

`3x+2y=12 \implies 2y=-3x+12 \implies y=-(3)/(2)x+6\\\\3x-2y=12 \implies 2y-3x=-12 \implies 2y=3x-12 \implies y=(3)/(2)x-6`

From this, we see that equation 1 is the answer.