Question

Which is an equation of a line that is perpendicular to the graph of 9x-3y=-10?

A. 3x-y=10

B. 4x+12y=11

C. 5x-15y=6

D. 6x+2y=9

Answer 1

`4x + 12y = 11`

Explanation:

`9x - 3y = -10`

`-3y = -10 - 9x`

`3y = 10 + 9x`

`3y = 9x + 10`

`y = 3x + 10/3`

the gradient of this graph is `3`.

to find the gradient of the perpendicular, find the negative reciprocal.

the negative reciprocal is what a number must be multiplied by to make `-1`.

`3 * -1/3 = -1`

the negative reciprocal of `3` is `-1/3`.

this means that the gradient of a graph perpendicular to `y = 3x + c` is `-1/3`.

for the perpendicular of `9x - 3y = 10`, `y = -1/3x + c`.

`4x + 12y = 11`

`12y = -4x + 11`

`y = -4/12 x + 11/12`

`y = -1/3x + 11/12`

this is in the form `y = mx+c`, where `m = -1/3` and `c = 11/12`.

Answer 2

B

Explanation:

As they have not defined a point the perpendicular line should pass through we only need one thing to compare against. That is the gradient.

given: `9x-3y=-10`

Writing this in the form `y=mx+c` we have: `y=9/3x+10/3`

Where `m=9/3=+3`

Thus the gradient of the line perpendicular to this one is

`(-1)xx1/m = -1/3`

We just need to hunt for this in the given choices.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`A->y=+3x-10 color(red)(larr" Fail. We need "-1/3x`

`B->y=-4/12x+11/12 color(green)(larr" Works." =-4/12=-1/3`

`C->y=+5/15x-6/10 color(red)(larr" Fail. We need "-1/3x`

`D->y=-6/2+9/2 color(red)(larr" Fail. We need "-1/3x`