Question

What could be the equation of a line parallel to the line `7x-12y= -32`?

Answer 1

`y=7/12x+"any y-intercept"`

Explanation:

What we want to do first is to get the equation in the form of `y=mx+b`.

Let's do that!

`7x-12y= -32`

Begin by subtracting `7x` from both sides:

`cancel(7x-7x)-12y= -7x-32`

Now divide both sides by `-12`:

`cancel(-12y)/cancel(-12)= (-7x-32)/-12`

`y=7/12x-32/12`

Here's the thing now, parallel lines have equal slopes. So, we simply just use the same slope when writing a new equation of a line.

`y=7/12x+b`

Since the question asked you what could be a line that is parallel you can add any `b` value otherwise known as the `"y-intercept"`.