A line of best fit describes the trend through scattered measurements, so its equation should match the drawn line rather than any one dot. Read where the line crosses the vertical axis, then use two positions on the line to find its slope, the change in time per practice session. A nearby dot can give a different slope.
Hints
- Hint 1
Each dot is one measured result, but the line of best fit represents the overall trend. For its equation, read two positions on the drawn line, even if neither position has a dot.
- Hint 2
The vertical intercept is the line’s predicted time when the number of practice sessions is . Where does the drawn line meet the vertical axis?
- Hint 3
The slope is the change in time divided by the change in sessions. Use the same two positions on the line for both changes, and check whether the slope should be positive or negative.
Step-by-step
Read the fitted line’s intercept and slope
Step 1Read two positions on the line
The drawn line passes near and , where each pair gives practice sessions first and time in seconds second. Use positions on the drawn line, not individual data dots. A dot near is higher than the line there.
- Step 2
Find the predicted time at zero sessions
The vertical intercept is the time the line predicts when . Since the line passes near , that starting prediction is about seconds.
- Step 3
Find the time change per session
The slope is the change in seconds divided by the change in sessions. From to , type in Desmos. It shows , so the line predicts about fewer seconds per session.
- Step 4
Write the fitted line’s equation
In slope-intercept form, , is the time change per session and is the time at zero sessions. Use the negative slope and the intercept you found: . This models the predicted typing time in seconds after practice sessions. Choice A.