To write the equation in slope intercept form, you need to solve the equation (in standard form) for y, it means, clear y from the equation:
[tex]\begin{gathered} 15x-8y=-4 \\ -8y=-15x-4 \\ y=-\frac{15}{-8}x-\frac{4}{-8} \\ y=\frac{15}{8}x+\frac{1}{2} \end{gathered}[/tex]The slope intercept form is 15/8x+1/2