1. **State the problem:** Find the x-intercept and y-intercept of the linear equation $$5x + 3y = 15$$. 2. **Recall the definitions:** - The x-intercept is the point where the line crosses the x-axis, so $$y = 0$$. - The y-intercept is the point where the line crosses the y-axis, so $$x = 0$$. 3. **Find the x-intercept:** Set $$y = 0$$ in the equation: $$5x + 3(0) = 15$$ $$5x = 15$$ Divide both sides by 5: $$x = \frac{15}{5} = 3$$ So, the x-intercept is at the point $$(3, 0)$$. 4. **Find the y-intercept:** Set $$x = 0$$ in the equation: $$5(0) + 3y = 15$$ $$3y = 15$$ Divide both sides by 3: $$y = \frac{15}{3} = 5$$ So, the y-intercept is at the point $$(0, 5)$$. 5. **Final answer:** - x-intercept: $$(3, 0)$$ - y-intercept: $$(0, 5)$$ These points tell us where the line crosses the axes, which is useful for graphing and understanding the behavior of the linear equation.