A chain of communication satellites near an asteroid belt drifted out of alignment, interrupting messages across the region. Emek and Tara examined graphs of the transmission paths, each represented by a linear equation. They compared the slopes to determine which paths had the correct direction and used the y-intercepts to identify the proper starting positions. After matching each graph to its corresponding satellite link, they recalibrated the network. Their careful analysis restored communication between every station, allowing navigation and research data to flow across the asteroid belt once again.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Compare the equation with the form y = mx + b.
One satellite transmission path is represented by the equation y = -2x + 5. Which statement correctly describes this path?
Slope = 5, y-intercept = -2Slope = -2, y-intercept = 5Slope = 2, y-intercept = -5Slope = -5, y-intercept = 2Correct! The slope is -2 and the y-intercept is 5.
Check which number is multiplied by x and which is the constant term.
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Hint
Find the change in y and divide by the change in x.
A satellite link passes through the points (2, 3) and (6, 11). What is the slope of the transmission path?
Correct! The slope of the path is 2.
Subtract the coordinates carefully before dividing.
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Hint
Look for the equation with slope 3 and y-intercept -1.
The correct satellite path must start at y = -1 and have a slope of 3. Which equation should Emek and Tara choose?
y = -x + 3y = 3x + 1y = 3x - 1y = -3x - 1Correct! The equation has the required slope and starting position.
Check both the coefficient of x and the constant term.
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