Problem

Given the linear equation \(3x - 4y = 7\), find the slope of the line perpendicular to it.

Answer

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Answer

The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line. In this case, the negative reciprocal of \(\frac{3}{4}\) is \(-\frac{4}{3}\).

Steps

Step 1 ：First, we must convert the equation to slope-intercept form (\(y = mx + b\)), where \(m\) is the slope. We can do this by isolating \(y\) in the equation.

Step 2 ：The equation becomes \(y = \frac{3}{4}x - \frac{7}{4}\), so the slope of the given line is \(\frac{3}{4}\).

Step 3 ：The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line. In this case, the negative reciprocal of \(\frac{3}{4}\) is \(-\frac{4}{3}\).

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