A drawn line of best fit models the trend, while the dots show individual observations. Use two marked points on the line to find its slope, the change in fish per week; Desmos can evaluate that fraction. Then read where the line crosses the vertical axis to complete . Use the line, not nearby dots.
Hints
- Hint 1
A line of best fit follows the overall pattern but need not pass through every measured dot. Use points on the drawn line, not nearby survey observations, to find the equation.
- Hint 2
The slope is the change in fish divided by the change in weeks. Subtract the coordinates in the same order on top and bottom. Where does the line cross the vertical axis?
Step-by-step
Find the slope and intercept from the line
Step 1Separate the line from the observations
The labeled and sit on the fitted line. The nearby dots at and are observations, the actual survey counts. Use the labeled line points to find the model's equation.
- Step 2
Find the fish gained per week
The slope is the change in fish divided by the change in weeks. Subtract in the same order for both coordinates. Type in Desmos; it shows . So the line predicts more fish for each additional week.
- Step 3
Read the starting value
At , the drawn line crosses the vertical axis at . That's its -intercept, : the model's predicted fish count when restoration began. Don't take the starting value from a survey dot.
- Step 4
Write the model
Put both values from the line into slope-intercept form, :
This models the predicted number of fish after weeks. Choice A.