Question

How do you write the equation of a line that is parallel to `2y = 3x + 6`?

Answer 1

`y=3/2x+b`

Explanation:

Parallel lines have equal slopes.

To find a line parallel to `2y=3x+6`, find the slope of the line.

The slope can be found by putting the line into `y=mx+b` form, where `m` is the slope of the line.

To put the line in `y=mx+b` form, divide everything by `2`.

`y=3/2x+3`

Therefore, `m=3/2` and the slope of the line is `3/2`.

Any line parallel to this line will also have a slope of `3/2`, but can be raised to any point.

This can be written as: `y=3/2x+b`, because the `b` doesn't interfere with the slope—it only raises the line up and down.