Question

What is the slope of a line perpendicular to the line whose equation is2x + 10y = 20. Fully simplify your answer.

Answer 1

For two lines to be perpendicular, if you multiply their slopes, the answer should be -1.

The first thing we need to do is to find the slope of this equation. Given that the equation of the slope is y=mx + b and m = slope,

`2x+10y=20`
`10y=-2x+20`
`(10y)/(10)=(-2x+20)/(10)`
`y=-(1)/(5)+2`

Given this equation, we now have a slope of -1/5.

Since we need the product of two slopes to be -1, we divide -1 by -1/5.

`m_1=-(1)/(5);m_2=?`
`m_1m_2=-1`
`-(1)/(5)m_2=-1`
`(-(1)/(5)m_2)/(-(1)/(5))=(-1)/(-(1)/(5))`
`m_2=5`

Therefore, in order for an equation to be perpendicular to 2x + 10y = 20, it must have a slope of 5.