A scatterplot can show both measured dots and a linear model, the straight line used to represent their trend. To find the model’s equation, use two points on the drawn line to find its slope, then use one of those points to find its altitude at time . A nearby dot may not lie on the model, and a marked point’s altitude is not the starting altitude unless its time is .
Hints
- Hint 1
The labeled points are on the drawn line, while the other dots are measurements that may miss it. Use the labeled points to find the slope, the change in altitude for each additional minute.
- Hint 2
Slope is rise over run: divide the altitude change by the matching time change. Subtract the points in the same order on top and bottom. How many meters does the line rise per minute?
- Hint 3
In , the -intercept is the altitude when . Put a labeled point into the equation to find it; neither labeled point has a time of .
Step-by-step
Find the slope, then the intercept
Step 1Find the line’s slope
Use the labeled points on the drawn line, and , rather than nearby measured dots. The slope is the altitude change divided by the time change, so type in Desmos. It shows , meaning the line rises meters per minute. Use points on the model line, not dots near it.
- Step 2
Find the altitude at time zero
Write the line in slope-intercept form , where is its altitude at . Because is on the line, put , , and the slope into that form:
Type in Desmos. The tells Desmos to find ; under PARAMETERS, it shows . The is not the intercept because it occurs at minute .
- Step 3
Write the model’s equation
Put both values into :
The drawn line models an altitude of meters at time and an increase of meters per minute. Choice A.