To estimate the average rate of change from \( x = 3.1 \) to \( x = 5.89 \), you would typically need to find the values of the solid line and the solid curve at those \( x \) values and then use the formula:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
where \( a = 3.1 \) and \( b = 5.89 \).
Without the actual image or values from the curve and line, I can't get the exact numbers. However, based on the options you provided, if you have estimated the values from the graph at these points, you can plug them into the formula above to identify the correct answer.
If you followed these steps and found a value close to one of the possible responses (0.5, -0.17, 6, or 0.17), that would lead you to your answer. If you're unsure, you may want to check your calculations or re-evaluate how the line and curve behave in that interval.
Can you provide more details or the estimated end values at \( x = 3.1 \) and \( x = 5.89 \) from the graph?