1. **Problem Statement:** We need to find the slopes of the missing line segments to complete the Christmas tree shape, which extends up to $y=23$. We will use the point-slope formula to find the slopes of the lines connecting given points. 2. **Point-Slope Formula:** The formula to find the slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ This formula calculates the rate of change of $y$ with respect to $x$. 3. **Identify Points for Missing Slopes:** - The tree extends vertically up to $y=23$, so we consider points near the top segments. - From the data, the highest horizontal segment is at $y=20$ between $x=1$ and $x=2$, and $x=-2$ and $x=-1$. - We want to find slopes of lines connecting these points to the top point at $y=23$ (assumed at $x=0$ for symmetry). 4. **Calculate Slopes for Left Side:** - Points: $(x_1,y_1) = (-2,20)$ and $(x_2,y_2) = (0,23)$ - Slope: $$m = \frac{23 - 20}{0 - (-2)} = \frac{3}{2} = 1.5$$ 5. **Calculate Slopes for Right Side:** - Points: $(x_1,y_1) = (2,20)$ and $(x_2,y_2) = (0,23)$ - Slope: $$m = \frac{23 - 20}{0 - 2} = \frac{3}{-2} = -1.5$$ 6. **Interpretation:** - The left side slope is positive $1.5$, indicating an upward incline to the right. - The right side slope is negative $-1.5$, indicating an upward incline to the left. 7. **Conclusion:** - The missing slopes to complete the Christmas tree top are $m=1.5$ on the left and $m=-1.5$ on the right, connecting the $y=20$ segments to the apex at $y=23$.