Question

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

3x+6y=-54.
Fully simplify your answer.

Answer 1

slope = 2

Explanation:

Slope-intercept form of a linear equation:
`y=mx+b`

(where m is the slope and b is the y-intercept)

Given equation:

`3x + 6y = -54`

Rearrange the given equation to make y the subject:

`\implies 6y=-3x=-54`

`\implies y=-(1)/(2)x-9`

Therefore, the slope of the given equation is
`-(1)/(2)`.

If two lines are perpendicular to each other, the product of their slopes will be -1.

Therefore, the slope (m) of the line perpendicular to the given equation is:

`\implies -(1)/(2) \cdot m=-1`

`\implies m=-1 / -(1)/(2)`

`\implies m=-1 \cdot-2`

`\implies m=2`