Question

given the equation 5y-3x=15 how would you determine another equation which would have: no solution, one solution, and infinitely many solutions

Answer 1

First, I would convert the equation to slope intercept form. 

That would be:  y = (3/5)x + 3  , now it will be easier to create the needed equations.

For no solution, keep the slope the same and change the y-intercept.
You could have: y = (3/5)x + 9

For one solution, all we have to do is change the slope.
You could have: y = (4/5)x + 3

For an infinite number of solutions, just multiply the entire equation by any number. Let's use the number 2.
2y = (6/5)x + 6