1. **State the problem:** Find the x-intercept and y-intercept of the line given by the equation $$-5x - 7y = 140$$. 2. **Recall the intercept 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: $$-5x - 7(0) = 140$$ $$-5x = 140$$ Divide both sides by $-5$: $$\cancel{-5}x = \frac{140}{\cancel{-5}}$$ $$x = -28$$ So the x-intercept is $$(-28, 0)$$. 4. **Find the y-intercept:** Set $x=0$ in the equation: $$-5(0) - 7y = 140$$ $$-7y = 140$$ Divide both sides by $-7$: $$\cancel{-7}y = \frac{140}{\cancel{-7}}$$ $$y = -20$$ So the y-intercept is $$(0, -20)$$. 5. **Summary:** - x-intercept: $$(-28, 0)$$ - y-intercept: $$(0, -20)$$ Note: The problem's mention of $\sqrt{x}$ for intercepts is incorrect; intercepts are coordinates, not square roots of $x$.