1. **State the problem:** We are given the equation of the line of best fit for speed limit $y$ based on houses per mile $x$ as $$y = -\frac{1}{2}x + 45.$$ We need to check which statement is true: - A road with 32 houses per mile would likely have a speed limit of about 30 miles per hour. - A road with 12 houses per mile would likely have a speed limit of about 50 miles per hour. 2. **Use the formula:** The speed limit $y$ is calculated by substituting the number of houses per mile $x$ into the equation: $$y = -\frac{1}{2}x + 45$$ 3. **Calculate speed for 32 houses per mile:** $$y = -\frac{1}{2} \times 32 + 45 = -16 + 45 = 29$$ So, the speed limit is about 29 miles per hour, which is close to 30. 4. **Calculate speed for 12 houses per mile:** $$y = -\frac{1}{2} \times 12 + 45 = -6 + 45 = 39$$ So, the speed limit is about 39 miles per hour, not 50. 5. **Conclusion:** The first statement is true: a road with 32 houses per mile would likely have a speed limit of about 30 miles per hour. The second statement is false because the speed limit for 12 houses per mile is about 39, not 50. **Final answer:** The statement "A road with 32 houses per mile would likely have a speed limit of about 30 miles per hour" is true.