Question 32·Medium·Two-Variable Data: Models and Scatterplots
A scatterplot shows the relationship between the time since a candle was lit, (in minutes), and the candle’s height, (in centimeters). A line of best fit is also shown.
Based on the line of best fit, which choice is closest to the predicted value of when the candle’s height is centimeters?
When a line of best fit is drawn, treat it as a linear model. Read two convenient points on the line to find the slope and intercept, write , and then substitute the given value (here ) and solve for the requested variable.
Hints
Use the line of best fit
The prediction should come from the line of best fit that is drawn, not from any single data point.
Find an equation for the line
Choose two clear points on the line (ideally where it hits grid intersections) and compute the slope to write an equation like .
Solve for when
After you have an equation for the line, replace with and solve the resulting equation for .
Desmos Guide
Enter the line using two points
In Desmos, compute the slope with (6-16)/(20-0) and note that the -intercept is , so the model is y=-0.5x+16.
Find where the line reaches a height of 10
Enter y=10 as a second equation. Use the intersection point of y=-0.5x+16 and y=10 to read the corresponding -value.
State the predicted time
Use the -coordinate of the intersection as the predicted time when the candle’s height is centimeters.
Step-by-step Explanation
Read two points on the line of best fit
From the graph, the line of best fit passes through and .
Write an equation for the line
Compute the slope:
Since the line crosses the -axis at , an equation for the line is
Set and solve for
Substitute and solve:
So the predicted value of is .