Question

Write the equation of the line that is perpendicular to the line 2x − 3y = 3 and passes through the point (−8, 2).

Answer 1

Hint: Perpendicular lines have opposite reciprocal slopes. A line of slope \(m\) has a perpendicular line of slope \(-\dfrac{1}{m}\).

Answer 2

Step one: Find the slope of the line you have. In this case, it's \(\frac23\).
Step two: Take the reciprocal, and reverse the sign. This gives us \(-\frac32\).
Step three: With that slope, you'll be able to write all perpendicular lines in this form: \(3x+2y=z\), for some number \(z\). You can see a convenient trick here: to find a perpendicular, we simply swapped the coefficients of the \(x\) and \(y\) terms, and reversed the sign in between them.
Step four: Plug in the point you were given to find the right-hand side of the equation (\(z\)). We have 3(-8)+2(2), which is -20, so our final solution is \(3x+2y=-20.\)