1. **State the problem:** We are given a linear regression equation $\hat{y} = 3.27 + 0.56x$ where $x$ is the stride length (m) and $\hat{y}$ is the predicted speed (m/s). We want to find the predicted speed when the stride length is $5.1$ m/s. 2. **Formula used:** The regression equation is of the form $$\hat{y} = b_0 + b_1 x$$ where $b_0$ is the intercept and $b_1$ is the slope. 3. **Substitute the given stride length:** Plug $x = 5.1$ into the equation: $$\hat{y} = 3.27 + 0.56 \times 5.1$$ 4. **Calculate the product:** $$0.56 \times 5.1 = 2.856$$ 5. **Add the intercept:** $$\hat{y} = 3.27 + 2.856 = 6.126$$ 6. **Interpretation:** The predicted speed for a stride length of 5.1 m is approximately $6.13$ m/s. This prediction is based on the linear relationship derived from the given data points.