What is the slope of a line perpendicular to the line whose equation is $\frac{x}4-\frac{y}5=1$? Express your answer as a common fraction.
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What is the slope of a line perpendicular to the line whose equation is (x/4)-(y/5)=1? Express your answer as a common fraction.
+2668 We have this equation: \(\frac{x}4-\frac{y}5=1\)
Subtract \({x \over 4}\) from both sides: \(-{y \over 5} = 1 - {x \over 4}\)
Multiply the entire equation by -5: \(y = {5 \over 4} x - 5\)
This means that the slope is \({5 \over 4}\), the slope of the line that is perpendicular to this is the negative reciprocal, or \(\color{brown}\boxed{-{4 \over 5}}\)
