Question

What is the equation of a line that passes through the point (8,1) and is perpendicular to the line whose equation is y= -2/3 x + 5?

A) 2X+3Y= 15
B) Y= -2/3x + 11
C) Y= 3/2x+ 11
D) y= 3/2x - 11

I am thinking its B but am not sure. I don't wanna retake this so I wanna be 100%. Thanks!!

Answer 1

The equation of this line would be y = 3/2x - 11, which is the answer D.

Explanation:

In order to find this equation we must first find the slope of the original line. The original slope (the coefficient of x) is -2/3, which means the new slope will also be 3/2 because perpendicular lines have opposite and reciprocal slopes. Now, we can use this slope along with the point in point-slope form to find the equation of the line.

y - y1 = m(x - x1)

y - 1 = 3/2(x - 8)

y - 1 = 3/2x - 12

y = 3/2x - 11