Question

What is the slope of a line perpendicular to the line whose equation is `y = -2/3x-5`?

Answer 1

The slope of a perpendicular line will be m = 3/2. To find the perpendicular gradient take the negative inverse of the original gradient.

Explanation:

The slope of a perpendicular line will be m = 3/2. To find the perpendicular gradient take the negative inverse of the original gradient.

By 'negative inverse' I mean change the sign and switch the numerator and denominator (the top and bottom of the fraction).
The original gradient there is m = - 2/3. Remember the line equation: y = mx + c.
To gain the perpendicular gradient change the - to +, move the 3 to the top and the 2 to the bottom. Now m = + 3 / 2 = 3/2