Question

Find an equation for the line satisfying the given conditions.
Through (3, 4) and parallel to 5x - 3y = 9.

Answer 1

y=(5/3)x-1

Answer 2

(3,4) is a coordinate where x = 3 and y = 4.

If the line you are looking for needs to be parallel to 5x-3y = 9, this means that it needs to have the same slope.

Your first step is to get the equation given to you into y=mx+b form.

5x - 3y = 9
-3y = -5x + 9
y = (5/3)x - 3

Your slope (m) is 5/3.
This needs to be the slope in your new equation. Also, if the line you are looking for passes through the point (3,4) , this means you can plug in these numbers as your x and y so you can solve for "b".

y = mx + b
4 = (5/3)(3) + b
4 = 5 + b
-1 = b.

Now you can plug the "m" and "b" that you have found into your y = mx + b equation.

y = (5/3)x -1