can enyone help me with this problem by tomorrow (write the following equation in slope-intercept form: 5x+2=3y)
Slope-intercept form looks like $\displaystyle y = mx + b$. When you get it in this form, the slope is just $\displaystyle m$ and the y-intercept is $\displaystyle b$.
So best thing is to solve for $\displaystyle y$.
$\displaystyle 5x+2 = 3y$;
$\displaystyle y = \frac{5x+2}{3} = \frac{5}{3}x+\frac{2}{3}$.