Question

How do you find an equation for a line parallel to `3x-4y=12`, with an `x`-intercept of 6?

Answer 1

Rearrange in the form of y=mx+c before substituting in your solution.

Explanation:

`3x-4y=12`

`(+4y)(-12)`

`4y=3x-12`

`(/4)`

`y=3/4x-3`

We know that parallel lines have the same gradient and we looking at this equation we can see the gradient of the line is `3/4`.

We now know the gradient of our answer and we must now calculate the y-intercept.

Let the y-intercept be `c`.

We know the `x`-intercept is 6 and therefore `(6,0)` is a point on the graph. We now have enough information to solve.

`y=3/4x+c`

Sub in `x` and `y`

`0=(3/4)6+c`

`0=4.5+c`

`c=-4.5`

We now have our answer:

`y=3/4x-4.5`