Question

What is the equation of a line that passes through the point (−9, 10) and is perpendicular to the line y=3x−6?

Answer 1

y= -
`(1)/(3)`x +7

Explanation:

y=3x−6

1. to find the gradient of a perpendicular line we find the reciprocal of the original gradinet

so the reciprocal of 3 is -
`(1)/(3)` (we can check this by multiplying both the gradient and seeing if we get -1 -
`(1)/(3)` x 3= -1 )

so the gradient is -
`(1)/(3)`

2. we sub in the gradient -
`(1)/(3)` into the equation y=mx+c this give us

y= -
`(1)/(3)`x +c

3. to find the value of c we substitute in the coordinates (we then expand the brackets and then get c on its own)

y= -
`(1)/(3)`x +c

10= -
`(1)/(3)`(-9) +c

10=3+c

7=c

4. we sub in 7=c back to the equation y= -
`(1)/(3)`x +c this gives us

y= -
`(1)/(3)`x +7

5. so our final answer is

y= -
`(1)/(3)`x +7