During a planetary exploration mission, Emek and Luna monitored a rover sending signals back to the base station. As the rover moved farther across the planet's surface, the communication delay changed, and the team recorded the distance and delay as coordinate pairs. Emek and Luna plotted the points on a digital graph and checked whether they formed a linear pattern. They noticed that the delay increased at a steady rate, allowing them to create a model for future signal times. Using the graph, they predicted when communication might become difficult and adjusted the rover's route to keep the connection strong. The successful test helped the exploration team continue the mission safely.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Compare how much the delay changes when the distance increases.
During the rover test, the recorded points were (2,5), (4,9), (6,13), and (8,17), where x represents distance and y represents communication delay. What is the constant rate of change?
1234Correct! The delay increases by 4 when the distance increases by 2, so the rate of change is 4/2 = 2.
Check the change in both coordinates and divide the change in y by the change in x.
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Hint
Substitute x = 7 into the linear model.
The rover communication model is y = 2x + 1, where x is distance and y is delay. What is the predicted delay when the rover reaches a distance of x = 7?
Correct! The model gives y = 2*7 + 1 = 15.
Use the equation carefully and replace x with the given distance.
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Hint
A linear pattern must have equal changes in y for equal changes in x.
Emek and Luna checked two possible rover signal models. Model A has points (1,4), (2,7), (3,10). Model B has points (1,4), (2,8), (3,13). Which model should they choose as the linear communication model?
Model A because the delay increases by the same amount each timeModel B because its delays become largerModel B because it starts with the same first pointBoth models because all points increaseCorrect! Model A has a constant increase of 3 in the delay values, so it is linear.
A model is linear only when the rate of change stays constant.
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