Question

Passes through the point (-4, -3) and is perpendicular to the line -3x - 4y = 12.

Answer 1

y=
`(4)/(3)` x+
`(7)/(3)`

Explanation:

-3x-4y=12

1. First we need to get the equation in the form of y=mx+c to do this we add 3x to both sides and then divide it by -4 on each side to get

(add 3x to both sides) = -4y=3x+12

(divide each side by -4)= y= -
`(3)/(4)` x -3

2. to find the perpendicular gradient we find the reciprocal of the original gradient

the reciprocal of -
`(3)/(4)` is
`(4)/(3)`

3. we can check this by multiplying them and seeing of we get -1

-
`(3)/(4)` x
`(4)/(3)` = = -1

4. we then sub in the gradient
`(4)/(3)` in y=mx+c this gives us

y=
`(4)/(3)`x +c

5. to find the value of c we substitute the coordinates into the equation to get ( we do this by expanding the brackets and getting c on it own)

-3=
`(4)/(3)`(-4) +c

-3= -
`(16)/(3)` +c

`(7)/(3)`=c

6. we sub
`(7)/(3)`=c back into y=
`(4)/(3)`x +c this gives us

y=
`(4)/(3)`x +
`(7)/(3)`

7. Therefore our final answer is

y=
`(4)/(3)`x +
`(7)/(3)`