The slope intercept form of a equation is given by:
[tex]\begin{gathered} y=mx+b \\ where \\ m=Slope \\ b=y-intercept \\ \end{gathered}[/tex]So, for the line:
[tex]3x-5y=15[/tex]Let's solve for y:
[tex]\begin{gathered} \text{add 5y to both sides:} \\ 3x-5y+5y=15+5y \\ 3x=5y+15 \\ \text{subtract 15 from both sides:} \\ 3x-15=5y+15-15 \\ 5y=3x-15 \\ \text{divide both sides by 5:} \\ \frac{5y}{5}=\frac{3x-15}{5} \\ y=\frac{3}{5}x-3 \end{gathered}[/tex]So, from the resulting equation we can conclude:
[tex]\begin{gathered} m=Slope=\frac{3}{5} \\ b=y-intercept=-3 \end{gathered}[/tex]