Before a spacecraft launch, Emek and Luna entered the control room to repair the navigation system. The digital grid showed several calibration points recorded from test flights. The points followed a pattern: each time the horizontal position increased, the vertical position changed by the same amount. Emek and Luna used the coordinates to identify the linear relationship and plotted the points on the grid. After drawing the correct line through the data, they checked that the guidance path matched the planned route. The restored system calculated accurate directions, and the spacecraft was ready for a safe mission.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Compare the change in the y-values when the x-values increase by 1.
During calibration, the navigation points were (1,4), (2,6), and (3,8). What is the change in the vertical position each time the horizontal position increases by 1?
1234Correct! The vertical values increase from 4 to 6 and from 6 to 8, so the change is 2.
Check how much the vertical coordinate changes between consecutive points.
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Hint
Replace x with 5 in the rule and calculate the value of y.
The navigation system follows the rule y = 3x + 2. What is the y-coordinate when the horizontal position is x = 5?
Correct! Using y = 3*5 + 2 gives y = 17.
Use the given rule carefully and substitute the correct x-value.
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Hint
Look for the same change in y for every increase of 1 in x.
Emek and Luna plotted points from a test flight. Which set of points shows a linear relationship with a constant rate of change?
(1,3), (2,6), (3,9)(1,2), (2,5), (3,9)(1,4), (2,4), (3,5)(1,1), (2,3), (3,7)Correct! The y-values in the first set increase by 3 each time, showing a constant rate of change.
A linear relationship requires the same change in y for equal changes in x.
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