Writing Linear Functions Unit Test
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Question
Two freight trucks are traveling to the same destination, and each are traveling at a constant speed. Truck A is 187
miles away from its destination at 9 a.m., one hour after leaving from its origin, and is 99
miles away from the destination at 10:36 a.m. Truck B started traveling to its destination at 6:30 a.m. Truck B is 248
miles away at 8:30 a.m. and 155
miles away at 10 a.m. Analyze each situation to determine a function that finds the distance to the destination for each truck based on the time in hours after starting the trip from the origin to the destination. Then use the functions to determine which truck will arrive first to its destination.(4 points)
Math Short Answer Rubric (4 points)
Points Awarded Criteria
4
The answer is clear and correct.
The answer shows that the student used problem-solving skills and reasoning.
All work is shown or explained.
3
The answer is mostly correct. The student made small errors while solving.
The answer shows that the student used some problem-solving skills and reasoning.
Most work is shown or explained.
2
The answer is partially correct. The student made errors while solving.
The answer shows that the student used some problem-solving skills or reasoning.
Some work is shown or explained.
1
The answer is incorrect. The student made errors while solving.
The answer shows little problem-solving skills or reasoning.
Little or no work is shown.
0 The question is not answered.
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To determine the functions for each truck, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept.
For Truck A:
We have two data points: (1, 187) and (1.6, 99).
The slope (m) can be calculated as (99 - 187) / (1.6 - 1) = -88 / 0.6 = -146.67.
Now we can substitute one of the points into the equation to find the y-intercept (b):
187 = -146.67(1) + b
187 = -146.67 + b
b = 333.67
Therefore, the equation for Truck A is y = -146.67x + 333.67.
For Truck B:
We have two data points: (2.5, 248) and (4, 155).
The slope (m) can be calculated as (155 - 248) / (4 - 2.5) = -93 / 1.5 = -62.
Substituting one of the points into the equation to find the y-intercept (b):
248 = -62(2.5) + b
248 = -155 + b
b = 403
Therefore, the equation for Truck B is y = -62x + 403.
Now we can determine which truck will arrive first to its destination by comparing the y-values of each equation at the same time.
For example, if we want to compare the distances at 10:30 a.m. (1.5 hours after Truck A started and 4 hours after Truck B started), we can substitute x = 1.5 into both equations and compare the y-values:
For Truck A: y = -146.67(1.5) + 333.67 = 113.33
For Truck B: y = -62(1.5) + 403 = 312
Since 113.33 is less than 312, Truck A will arrive first to its destination.