1. **State the problem:** Find the x-intercept, y-intercept, and slope of the line given by the equation $$3x + 2y = 6$$. 2. **Formula and rules:** - The x-intercept is found by setting $$y = 0$$ and solving for $$x$$. - The y-intercept is found by setting $$x = 0$$ and solving for $$y$$. - The slope $$m$$ of a line in standard form $$Ax + By = C$$ is $$m = -\frac{A}{B}$$. 3. **Find the x-intercept:** Set $$y = 0$$ in the equation: $$3x + 2(0) = 6 \implies 3x = 6 \implies x = \frac{6}{3} = 2$$ So, the x-intercept is at $$(2, 0)$$. 4. **Find the y-intercept:** Set $$x = 0$$ in the equation: $$3(0) + 2y = 6 \implies 2y = 6 \implies y = \frac{6}{2} = 3$$ So, the y-intercept is at $$(0, 3)$$. 5. **Find the slope:** Using $$m = -\frac{A}{B}$$ where $$A=3$$ and $$B=2$$: $$m = -\frac{3}{2}$$ **Final answers:** - x-intercept: $$(2, 0)$$ - y-intercept: $$(0, 3)$$ - slope: $$-\frac{3}{2}$$