Hi there!
Slope intercept form is [tex]y=mx+b[/tex]. To do this, we just need to isolate y. This can be done by first moving everything that doesn't involve a y to the other side, and then dividing by the coefficient:
[tex]16x+17y=-2[/tex]
[tex]17y=-2-16x[/tex]
[tex]y=-\frac{2}{17}-\frac{16}{17}x[/tex]
And there you have your answer, just above.
Hope this helps, feel free to let me know if you have any additional questions about this specific problem!