1. **State the problem:** Determine the relationship between the lines given by the equations: $y = 3x - 5$ and $5x + 4y = -3$ 2. **Rewrite the second equation in slope-intercept form:** Solve for $y$: $$5x + 4y = -3$$ $$4y = -5x - 3$$ $$y = \frac{-5}{4}x - \frac{3}{4}$$ 3. **Compare slopes:** The first line has slope $m_1 = 3$. The second line has slope $m_2 = -\frac{5}{4}$. 4. **Analyze slopes:** Since $m_1 = 3$ and $m_2 = -\frac{5}{4}$ are not equal, the lines are not parallel. 5. **Check if lines coincide:** Lines coincide if they have the same slope and same intercept, which is not the case here. 6. **Conclusion:** The lines have different slopes, so they intersect at exactly one point. Therefore, the lines are **intersecting**.