If a line on a graph has a slope of m, what is the slope of a line that is perpendicular to it?

• A. -1/m
• B. m
• C. 1/m
• D. -m

Answer: (A)

Verified step by step guidance

1. Recall that the slope of a line, denoted as \(m\), represents the rate of change of the vertical coordinate with respect to the horizontal coordinate on a graph.
2. Understand that two lines are perpendicular if the angle between them is 90 degrees, which implies a specific relationship between their slopes.
3. Use the property that the slope of a line perpendicular to another line with slope \(m\) is the negative reciprocal of \(m\).
4. Express the slope of the perpendicular line mathematically as \(-\frac{1}{m}\).
5. Conclude that if the original line has slope \(m\), then the slope of the line perpendicular to it is \(-\frac{1}{m}\).