1. **State the problem:** Find the x- and y-intercepts of the line given by the equation $$3x - 4y = 12$$ and use them to sketch the line. 2. **Recall intercept definitions:** - The x-intercept is where the line crosses the x-axis, so $y=0$. - The y-intercept is where the line crosses the y-axis, so $x=0$. 3. **Find the x-intercept:** Set $y=0$ in the equation: $$3x - 4(0) = 12$$ $$3x = 12$$ Divide both sides by 3: $$\cancel{3}x = \cancel{3}4$$ $$x = 4$$ So the x-intercept is at the point $(4,0)$. 4. **Find the y-intercept:** Set $x=0$ in the equation: $$3(0) - 4y = 12$$ $$-4y = 12$$ Divide both sides by $-4$: $$\cancel{-4}y = \cancel{-4}(-3)$$ $$y = -3$$ So the y-intercept is at the point $(0,-3)$. 5. **Summary:** - x-intercept: $(4,0)$ - y-intercept: $(0,-3)$ 6. **Sketching the line:** Plot the points $(4,0)$ and $(0,-3)$ on the coordinate plane and draw a straight line through them. This line represents the equation $3x - 4y = 12$. This completes the solution.