From the image, the task involves analyzing a scatterplot and working with a trend line to make predictions. Let's break it down:

Problem Breakdown:

1. Draw a trendline:

   • This involves estimating the line of best fit through the data points in the scatterplot.

2. Write the equation for the trendline:

   • It looks like the slope $m = \frac{-35}{2}$ (calculated as $\Delta y / \Delta x$), and the y-intercept is approximately $105$.
   • The equation derived is $y = -\frac{35}{2}x + 105$.

3. Use the trendline for prediction:

   • The question asks for the response speed when study time is 6 minutes. Substitute $x = 6$ into the equation $y = -\frac{35}{2}x + 105$.

Calculations:

Substitute $x = 6$ into $y = -\frac{35}{2}x + 105$: $y = -\frac{35}{2}(6) + 105$ $y = -105 + 105 = 0$

So, the predicted response speed for 6 minutes of study time is 0 seconds.

Do you need more detailed explanations, or have additional questions?

Related Questions:

1. What does the slope of the trendline represent in this context?
2. How would you calculate the slope if the data points were slightly different?
3. Can you explain why the response speed decreases as study time increases?
4. How can we check if this trendline accurately models the data?
5. What would happen if we extend the trendline to $x > 6$?

Tip:

Always check the scatterplot visually to ensure the trendline equation makes sense for the data distribution.