1. **State the problem:** Find the x-intercept and y-intercept of the line given by the equation $$y + 1 = 3(x - 4)$$. 2. **Rewrite the equation in slope-intercept form:** $$y + 1 = 3x - 12$$ Subtract 1 from both sides: $$y = 3x - 12 - 1$$ $$y = 3x - 13$$ 3. **Find the x-intercept:** The x-intercept occurs where $$y = 0$$. Set $$y = 0$$ in the equation: $$0 = 3x - 13$$ Add 13 to both sides: $$13 = 3x$$ Divide both sides by 3: $$\cancel{3}x = \frac{13}{\cancel{3}}$$ $$x = \frac{13}{3}$$ So the x-intercept is $$\left(\frac{13}{3}, 0\right)$$. 4. **Find the y-intercept:** The y-intercept occurs where $$x = 0$$. Substitute $$x = 0$$ into the equation: $$y = 3(0) - 13$$ $$y = -13$$ So the y-intercept is $$(0, -13)$$. **Final answer:** - x-intercept: $$\left(\frac{13}{3}, 0\right)$$ - y-intercept: $$(0, -13)$$