Question

How do you write the slope of a line parallel to `4x -6y =-18`?

Answer 1

y = 2/3x + a (generic), y = 2/3x + 15 (one specific example)

Explanation:

First, you put the equation into the standard “slope/intercept” form.
4x -6y = -18 subtract 4x from both sides ; -6y = -18 -4x
-6y = -18 -4x divide both sides by -6 ; y = 2/3x + 3

In this standard form we see that the slope of the line (coefficient of x) is 2/3.

ANY line parallel to this one must thus also have a slope of 2/3.

ANY other combination of slope multiples and constant terms will therefore also be lines parallel to this one. For example: y = 2/3x + 15