1. **State the problem:** Find the x-intercept and y-intercept of the line given by the equation $$2x + 6y = -6$$ and use these intercepts to graph the line. 2. **Recall 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: $$2x + 6(0) = -6$$ $$2x = -6$$ Divide both sides by 2: $$\cancel{2}x / \cancel{2} = -6 / 2$$ $$x = -3$$ So the x-intercept is $(-3, 0)$. 4. **Find the y-intercept:** Set $x=0$ in the equation: $$2(0) + 6y = -6$$ $$6y = -6$$ Divide both sides by 6: $$\cancel{6}y / \cancel{6} = -6 / 6$$ $$y = -1$$ So the y-intercept is $(0, -1)$. 5. **Graph the line using intercepts:** Plot the points $(-3, 0)$ and $(0, -1)$ on the coordinate plane. Draw a straight line through these two points to represent the equation. **Final answer:** - x-intercept: $(-3, 0)$ - y-intercept: $(0, -1)$