Question

What is the slope of a line perpendicular to y=-(7)/(4)x

Answer 1

`(4)/(7)`

Explanation:

Given

y = -
`(7)/(4)` x ( in the form y = mx , where m is the slope )

slope m = -
`(7)/(4)`

Given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(7)/(4) )` =
`(4)/(7)`

Answer 2

Answer: 4/7

This is because the original line has slope -7/4. We flip the fraction and the sign, ie take the negative reciprocal, to get the perpendicular slope.

Flipping the fraction goes from -7/4 to -4/7. Then it flips to positive to get 4/7

Notice that multiplying the original and perpendicular slopes together gets us -1

(-7/4)*(4/7) = -1

This applies to any pair of perpendicular lines as long as neither line is vertical and neither is horizontal.