The slope intercept form is given by:
[tex]\begin{gathered} y=mx+b \\ \text{where:} \\ m=\text{slope} \\ b=y-\text{intercept} \\ \text{for:} \\ -3x+15y=-18 \\ \text{solve for y:} \\ \text{add 3x to both sides:} \\ -3x+15y+3x=-18+3x \\ 15y=-18+3x \\ \text{divide both sides by 15:} \\ \frac{15y}{15}=-\frac{18}{15}+\frac{3x}{15} \\ y=\frac{1}{5}x-\frac{6}{5} \end{gathered}[/tex]