Problem 42

Question

What is the slope of a line that is perpendicular to the line whose equation is \(A x+B y+C=0, A \neq 0\) and \(B \neq 0 ?\)

Step-by-Step Solution

Verified
Answer
The slope of a line perpendicular to the line with the equation \(Ax + By + C = 0\) is \(B/A\).
1Step 1: Determining the slope of the given line
The slope of a line with equation \(Ax+By+C=0\) is \(-A/B\). So, the slope of this given line is \(-A/B\).
2Step 2: Finding the slope of the perpendicular line
The slope of a line perpendicular to a line with slope \(m\) is \(-1/m\). This is found by flipping the fraction and changing the sign. Hence, the slope of a line perpendicular to our given line is \(-1/(-A/B) = B/A\).