1. **State the problem:** Graph the linear equation $5x - 3y = 15$. 2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. **Isolate $y$:** $$5x - 3y = 15$$ Subtract $5x$ from both sides: $$-3y = -5x + 15$$ Divide both sides by $-3$: $$y = \frac{\cancel{-3}y}{\cancel{-3}} = \frac{-5x + 15}{-3} = \frac{\cancel{-5}x}{\cancel{-3}} - \frac{15}{3} = \frac{5}{3}x - 5$$ 4. **Interpret the slope and intercept:** - Slope $m = \frac{5}{3}$ means the line rises 5 units for every 3 units it runs to the right. - Y-intercept $b = -5$ means the line crosses the y-axis at $(0, -5)$. 5. **Find the x-intercept:** Set $y=0$ in the original equation: $$5x - 3(0) = 15 \Rightarrow 5x = 15 \Rightarrow x = 3$$ So the x-intercept is at $(3, 0)$. 6. **Summary:** The line passes through points $(0, -5)$ and $(3, 0)$ with slope $\frac{5}{3}$. Final answer: $$y = \frac{5}{3}x - 5$$