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.

Guest Jul 17, 2022

#2**0 **

Ok!

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.

Guest Jul 17, 2022

#3**+1 **

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 \(\color{brown}\boxed{-{4 \over 5}}\)

BuilderBoi Jul 17, 2022