1. **State the problem:** We are given data relating the number of automatic weapons (in thousands) $x$ to the number of murders per 100,000 residents $y$. The data is modeled by the linear equation $$\hat{y} = 0.84x + 4.11.$$ 2. **Understand the linear model:** The equation $$\hat{y} = 0.84x + 4.11$$ means that for each increase of 1 thousand automatic weapons, the predicted murders per 100,000 residents increase by 0.84. The constant term 4.11 represents the predicted murders when $x=0$. 3. **Interpret the slope and intercept:** - Slope ($0.84$): For every additional 1 thousand automatic weapons, murders increase by 0.84 per 100,000 residents. - Intercept ($4.11$): When there are no automatic weapons ($x=0$), the predicted murder rate is 4.11 per 100,000 residents. 4. **Use the model to predict:** For example, if $x=5$ (5 thousand weapons), then $$\hat{y} = 0.84(5) + 4.11 = 4.2 + 4.11 = 8.31.$$ This means about 8.31 murders per 100,000 residents are predicted. 5. **Graph shape description:** The graph is a straight line with positive slope 0.84, crossing the $y$-axis at 4.11. It rises gently from left to right, indicating a positive correlation between weapons and murders. **Final answer:** The linear model $$\hat{y} = 0.84x + 4.11$$ predicts murders per 100,000 residents based on thousands of automatic weapons.