Inside a space laboratory orbiting Earth, Emek and Luna examined a solar array that was producing unexpected amounts of power. The engineers had recorded energy output at different operating settings, but they needed to find the model that best matched the data. Emek and Luna plotted each measurement on a coordinate grid and compared several possible lines. They looked at how the power changed as the settings increased and identified the graph that followed the same linear pattern as the recorded points. After selecting the correct model, they shared the results with the engineers, who adjusted the solar array settings to produce energy more efficiently.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Find how much y changes when x increases by 1 and check the starting pattern.
The solar array data included the points (1,5), (2,10), (3,15), and (4,20). Which equation represents the linear relationship between the operating setting x and the energy output y?
y = 5xy = x + 5y = 2x + 5y = 5x + 5Correct! Each increase of 1 in x increases y by 5, so the relationship is y = 5x.
Check the constant rate of change between the data points.
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Hint
Substitute the value of x into the equation and calculate y.
The engineers found that the solar array model was y = 4x + 3. What is the energy output when the operating setting is x = 6?
Correct! Using y = 4*6 + 3 gives y = 27.
Use the equation given in the question and replace x with 6.
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Hint
Compare the changes between consecutive y-values for each model.
Emek and Luna compared two possible models for the solar array. Model A has points (2,8), (3,12), and (4,16). Model B has points (2,8), (3,13), and (4,19). Which model better represents a linear pattern with a constant rate of change?
Model B because its outputs are largerModel A because its output increases by the same amount each timeModel B because it has more energy outputBoth models because all outputs increaseCorrect! Model A increases by 4 each time, so it has a constant rate of change.
A linear pattern requires equal changes in y for equal changes in x.
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