What is the x-intercept of the line perpendicular to the line defined by 3x-2y = 6 and whose y-intercept is 2?

Question

What is the x-intercept of the line perpendicular to the line defined by 3x-2y = 6 and whose y-intercept is 2?

Answer 1

3x-2y = 6

solve for y

2y = 3x-6

y = 3x/2 -3 (3/2) is the slope. change its sign and invert it to get -2/3 as the slope of the perpendicular line

y = -2x/3 + b, where b = 2, the y intercept

y =-2x/3 + 2 is the perpendicular line with y intercept = 2

It's x intercept is found by setting y=0

0 = -2x/3 + 2

2x/3 = 2

x/3 = 1

x = 3 = the x intercept of the perpendicular line

or the point (3,0)