1. **State the problem:** We need to find the equation of a line with slope $-\frac{3}{5}$ that passes through the point $(-3,3)$. The equation should be in slope-intercept form $y=mx+b$. 2. **Recall the slope-intercept form:** The general form is $$y=mx+b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Use the point-slope form to find $b$:** Substitute the slope $m=-\frac{3}{5}$ and the point $(-3,3)$ into the equation: $$3 = -\frac{3}{5} \times (-3) + b$$ 4. **Simplify the multiplication:** $$3 = \frac{9}{5} + b$$ 5. **Solve for $b$:** $$b = 3 - \frac{9}{5} = \frac{15}{5} - \frac{9}{5} = \frac{6}{5}$$ 6. **Write the final equation:** $$y = -\frac{3}{5}x + \frac{6}{5}$$ This is the equation of the line in slope-intercept form with slope $-\frac{3}{5}$ passing through $(-3,3)$.