You are describing one type of problem in the title and another in the body.
I'll do the first
For the title, just make y=0 then solve for x. Plot the point (x,0).
Next make x=0 then solve for y. Plot the point (0,y).
Connect them with a line and you have the plot.
3x=5y-15
3x=5*0-15
x=-5
The x intercept is (-5,0)
3*0=5y-15
y=3
the y intercept is (0,3)
Connect (-5,0) to (0,3)
For the body type of problem
solve for y to get the form
y=mx+b
Add 15 to both sides
3x+15=5y
swap sides
5y=3x+15
Divide by 5
y=(3/5)x+(15/5) =
.6X+3
Looking at the form, m (the slope) = .6 and b (the y intercept) = 3
That matches the y intercept you got in the first part. (0,3)
Draw a line from there (in both directions) that goes to the right 5 and up 3
