What is the slope of a line perpendicular to \(y = -3x + 7\)?
\(\tfrac{1}{3}\)
For a line in the form \(y = mx + c\), the slope is \(m\).
Here the given line is \(y = -3x + 7\), so its slope is \(m_1 = -3\).
Condition for perpendicular lines: the product of their slopes is −1, i.e., \(m_1 \times m_2 = -1\).
Substituting \(m_1 = -3\):
\(-3 \times m_2 = -1 \;\Rightarrow\; m_2 = \dfrac{-1}{-3} = \dfrac{1}{3}\)
Hence the perpendicular slope is \(\dfrac{1}{3}\).
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