Question

How do I write an equation of a line that is parallel to 2x-3y=15

Answer 1

The line given is -2x + 3y = 15, so we must rearrange:

=> 3y = 2x + 15
=> y = 2/3 x + 5

These two equations are EQUIVALENT, but one is in slope intercept form, the other isn't.

So in this case, gradient is 2/3 (or 2 units up, and 3 units across).

And we know that parallel lines have the same gradient. Hence, the general equation for lines parallel to it will be:

y = 2/3 x + n

where n can be any number (positive/negative, decimal/fraction/integer) except 5, which is original line.

For example, y = 2/3 x + 2