Question

What is the equation in standard form of a perpendicular line to y=3x+6 that passes through (5,-1)?

Answer 1

`y=-1/3x+2/3`

Explanation:

first, we need to identify the gradient of the line y=3x+6.
It is already written in the form y=mx+c, where m is the gradient.
the gradient is 3

for any line that is perpendicular, the gradient is `-1/m`
the gradient of the perpendicular line is `-1/3`

Using the formula `y-y_1=m(x-x_1)` we can work out the equation of the line.
substitute m with the gradient `-1/3`
substitute `y_1` and `x_1` with the coordinates given: (5,-1) in this case.
`y--1=-1/3(x-5)`
simplify to get the equation:
`y+1=-1/3(x-5)`
`y=-1/3x+5/3-1`

`y=-1/3x+2/3`