The scatterplot shows data for several solar-panel installations. The axes use scaled units, and the line of best fit is labeled in the graph.
Let be the total number of solar panels in an installation, and let be the monthly energy generated, in kilowatt-hours. Which choice gives the equation of the line of best fit in terms of and ?
For a line of best fit with scaled axes, first identify what one graph unit represents on each axis. Write the graph variables in terms of the requested actual variables, substitute into the displayed model, and then simplify. Convert both the slope and the intercept; the intercept is affected whenever the vertical axis is scaled.
Hints
Read the units carefully
The variables in the graph's equation do not represent individual panels and individual kilowatt-hours directly.
Express the graph variables
If is the actual number of panels, determine how to write the graph's -value in terms of . Do the same for and .
Substitute before simplifying
Replace and in the displayed line-of-best-fit equation with expressions involving and , then clear the denominator.
Desmos Guide
Use algebra first
Algebra is faster here because the key task is converting the units on both axes. Use Desmos to verify the conversion with a point on the displayed line.
Check a point on the line
Enter . At , the line has . From the axis labels, this represents panels and kilowatt-hours.
Test the candidate equations
Enter each answer choice using as the horizontal variable. At , only one choice gives , matching the converted point from the graph.
Step-by-step Explanation
Interpret the scaled axes
The graph uses to represent tens of panels, so . It uses to represent hundreds of kilowatt-hours, so .
Substitute into the graph's equation
The labeled line of best fit is . Substitute the scaled-variable expressions:
Write the model in actual units
Multiply both sides by :
This is choice C.