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Question: A coordinate plane showing the Speed of a Red Kangaroo. The x-axis shows Time in seconds and the y-axis shows Distance Traveled in feet. There is a straight line with a positive slope starting at (0, 0) and passing through point A at (3, 150), then point B at (4, 200) and continues through (7, 350). Red kangaroos can reach speeds up to 50 feet per second. Use the linear graph at the left to answer the questions. What is the change in y-values from Point A to Point B? What is the change in x-values from Point A to Point B? What is the rate of change of the linear function? feet per second
The change in y-values from Point A to Point B can be found by subtracting the y-coordinate of Point A from the y-coordinate of Point B. That is, 200 - 150 = 50 feet. The change in x-values from Point A to Point B can be found by subtracting the x-coordinate of Point A from the x-coordinate of Point B. That is, 4 - 3 = 1 second. The rate of change of a linear function is the change in the y value divided by the change in the x value (also known as the slope of the line). For this problem, it is 50 feet / 1 second = 50 feet per second. So the rate of change of the linear function is 50 feet per second. This indicates that the speed of the Red Kangaroo is consistent with the maximum speed stated.
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