During a long-range exploration mission, Emek and Tara discovered two navigation models predicting different spacecraft paths. Each model included linear equations and graphs describing the planned course. They compared the slopes to evaluate the direction of travel, checked the y-intercepts against the spacecraft's starting position, and analyzed where the lines intersected with key navigation checkpoints. One model failed to match the required trajectory, while the other agreed with every mission condition. Their careful reasoning prevented a navigation error and guided the spacecraft safely to its destination.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
In y = mx + b, check both the coefficient of x and the constant term.
The spacecraft must start at y = 4 and follow a path with slope -2. Which navigation model matches both conditions?
y = 2x + 4y = -2x - 4y = -2x + 4y = 4x - 2Correct! The model has slope -2 and y-intercept 4.
Try again. Check the required slope and starting position separately.
Next🎉 Congrats! You got this question!
Hint
At the intersection, the two expressions for y are equal.
Two navigation paths are modeled by y = 2x + 1 and y = -x + 10. What is the x-coordinate of their intersection point?
Correct! The paths intersect when x = 3.
Set the two equations equal and solve for x.
Next🎉 Congrats! You got this question!
Hint
Compare both the slopes and the y-intercepts.
Model A is y = 3x - 2, and Model B is y = 3x + 5. Tara says the paths will eventually meet because they have the same slope. Which conclusion is correct?
Tara is correct because equal slopes always make lines intersect.Tara is incorrect because the lines have different slopes.Tara is incorrect because the lines are parallel and have different y-intercepts.Tara is correct because both equations contain the number 3.Correct! Equal slopes with different y-intercepts produce parallel lines that never meet.
Try again. Lines with the same slope only coincide when their y-intercepts also match.
Next🎉🎉🎉🎉🎉🎉🎉🎉
🎉 Congrats! You finished this challenge set!
