1. **Problem statement:** We are given two functions: a line $f(x)$ (graph shown) and a quadratic function $g(x) = -x^2 - 3x - 5$. We need to find the intersection points of their graphs. 2. **Identify the line equation:** From the description, the line crosses the y-axis at about $-2$ and the x-axis at about $2$. The slope $m$ is calculated as: $$m = \frac{0 - (-2)}{2 - 0} = \frac{2}{2} = 1$$ So the line equation is: $$f(x) = x - 2$$ 3. **Set the functions equal to find intersections:** $$f(x) = g(x)$$ $$x - 2 = -x^2 - 3x - 5$$ 4. **Rearrange to form a quadratic equation:** $$x - 2 + x^2 + 3x + 5 = 0$$ $$x^2 + 4x + 3 = 0$$ 5. **Factor the quadratic:** $$x^2 + 4x + 3 = (x + 1)(x + 3) = 0$$ 6. **Solve for $x$:** $$x + 1 = 0 \Rightarrow x = -1$$ $$x + 3 = 0 \Rightarrow x = -3$$ 7. **Find corresponding $y$ values using $f(x)$:** $$f(-1) = -1 - 2 = -3$$ $$f(-3) = -3 - 2 = -5$$ 8. **Intersection points:** $(-1, -3)$ and $(-3, -5)$ **Final answer:** The graphs intersect at points $(-1, -3)$ and $(-3, -5)$.