Question

What is the slope of a line perpendicular to the line whose equation is

4x - 5y = 10. Fully simplify your answer. Pls help me tysm

Answer 1

Perpendicular lines have slopes that are opposite signs and reciprocals.

For example, the perpendicular slope to 2/3 is -3/2 (opposite sign and flipped upside-down).

The first step on your question is to find the slope of your line. You can do this by putting the equation into slope-intercept form:

`\begin{aligned}4x-5y &= 10\\[0.5em]-5y &= -4x+10\\[0.5em]y &= (4)/(5)x-2\endaligned}`

From this, we can see your slope is 4/5.

The perpendicular slope will be -5/4.