4. Given the table for x, time in minutes, and y, distance traveled:
x: time 8 5 7 2 9
y: distance 664 415 581 166 747
(4 points)
a. Every minute
656
meters are traveled.
b. Write an equation to show the relationship between x and y:
12y = x
.
c. This relationship is
non proportional
because the y-intercept is
(0, 0)
a. Every minute, 656 meters are traveled is incorrect as it does not match the given data. The correct answer should be "Every minute, approximately 82 meters are traveled" (calculated by finding the average of the distances traveled in each time period: (664+415+581+166+747)/5 ≈ 714.6).
b. The equation to show the relationship between x and y can be found using a linear regression analysis. By plotting the given data points and finding the line of best fit, the equation can be determined. However, the equation given (12y = x) is not correct as it does not match the given data.
c. We cannot determine if the relationship is proportional or non-proportional based on the given information. To determine if a relationship is proportional, we need to check if the ratio of y/x is constant for each data point. Without that information, we cannot conclude whether the relationship is proportional or not.
What is the Correct Answer
a. Every minute, approximately 82.4 meters are traveled (calculated by finding the average of the distances traveled in each time period: (664+415+581+166+747)/5 ≈ 714.6).
b. To find the equation that shows the relationship between x and y, we can use a linear regression analysis. Using the given data points, the equation is approximately y = 73.2x - 47.2.
c. We cannot determine if the relationship is proportional or non-proportional based on the given information. To determine if a relationship is proportional, we need to check if the ratio of y/x is constant for each data point. Without that information, we cannot conclude whether the relationship is proportional or not.
a. To find out how many meters are traveled every minute, we need to calculate the ratio of distance to time for each pair of values in the table.
For x = 8, y = 664:
Ratio = y / x = 664 / 8 = 83 meters/minute
For x = 5, y = 415:
Ratio = y / x = 415 / 5 = 83 meters/minute
For x = 7, y = 581:
Ratio = y / x = 581 / 7 = 83 meters/minute
For x = 2, y = 166:
Ratio = y / x = 166 / 2 = 83 meters/minute
For x = 9, y = 747:
Ratio = y / x = 747 / 9 = 83 meters/minute
From all these calculations, we can conclude that every minute, 83 meters are traveled.
b. To write an equation to show the relationship between x and y, we can use the values from the table to find the slope of the line passing through the points (0, 0) and (x, y).
Slope = (y2 - y1) / (x2 - x1)
For this case, we can take the point (0, 0) as the starting point, so (x1, y1) = (0,0) and (x2, y2) can be any of the given points.
Let's use the point (5, 415):
Slope = (415 - 0) / (5 - 0) = 415 / 5 = 83
So the equation relating x and y is y = 83x.
c. This relationship is non-proportional because the y-intercept is (0,0). In a proportional relationship, the y-intercept is always (0,0), but since this relationship has a non-zero y-intercept, it is non-proportional.
To find the answers to the questions, we can analyze the given data in the table.
a. To determine how many meters are traveled per minute, we can calculate the average distance traveled for all the given values of x (time) and y (distance).
Average distance traveled = (sum of all distances)/(number of data points)
Using the values from the table:
Average distance traveled = (664 + 415 + 581 + 166 + 747)/5 = 2573/5 = 514.6 meters
Therefore, every minute approximately 656 meters are traveled.
b. To write an equation that shows the relationship between x (time) and y (distance), we need to determine the pattern or trend in the data. One way to do this is by checking if the relationship is proportional or non-proportional.
If the relationship is proportional, it means that the ratio of y to x is constant for all values. To check this, we can calculate the ratio of y to x for each data point.
Ratios:
For x = 8, y = 664, ratio = 664/8 = 83
For x = 5, y = 415, ratio = 415/5 = 83
For x = 7, y = 581, ratio = 581/7 = 83
For x = 2, y = 166, ratio = 166/2 = 83
For x = 9, y = 747, ratio = 747/9 = 83
Since the ratio of y to x is the same for all data points, we can write the equation in the form: y = kx, where k is the constant ratio.
Substituting any of the data points, we get:
k = y/x = 664/8 = 83
Hence, the equation that shows the relationship between x and y is y = 83x.
c. To determine if the relationship is proportional or non-proportional, we can look at the y-intercept of the equation. The y-intercept represents the value of y when x is equal to zero.
In the equation y = 83x, when x = 0, y = 0.
Thus, the y-intercept is (0, 0). This signifies that the relationship is non-proportional.
Therefore, the answers are:
a. Every minute, 656 meters are traveled.
b. The equation showing the relationship between x and y is y = 83x.
c. This relationship is non-proportional because the y-intercept is (0, 0).