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 _ meters are traveled.
b. Write an equation to show the relationship between x and y: _
c. This relationship is _ y because the y-intercept is _
a. Every minute 83 meters are traveled.
b. Write an equation to show the relationship between x and y: y = 83x
c. This relationship is a linear relationship because the y-intercept is 0.
To find the answers, let's analyze the given table for x (time) and y (distance traveled):
x: time 8 5 7 2 9
y: distance 664 415 581 166 747
a. To find the distance traveled per minute, we need to calculate the difference in distance between consecutive values and divide it by the difference in time between those values.
For the first two data points:
Distance traveled in the first interval = 664 - 415 = 249
Time elapsed in the first interval = 8 - 5 = 3 minutes
Distance traveled per minute in the first interval = 249 / 3 = 83 meters
Similarly, for the second interval:
Distance traveled in the second interval = 581 - 166 = 415
Time elapsed in the second interval = 7 - 2 = 5 minutes
Distance traveled per minute in the second interval = 415 / 5 = 83 meters
Therefore, we can conclude that every minute, 83 meters are traveled.
b. To write an equation representing the relationship between x and y, we need to determine the pattern or formula connecting the time and distance variables.
Looking at the given data, it appears that the distance traveled depends on the time according to this equation:
y = mx + b
To find the values of m and b, we can choose any data point and substitute the values of x and y into the equation:
Using the first data point (8, 664), we get:
664 = m(8) + b
Substituting the second data point (5, 415), we get:
415 = m(5) + b
Now we have a system of two equations:
664 = 8m + b
415 = 5m + b
By solving this system of equations, we can find the values of m and b.
Subtracting the second equation from the first equation, we get:
664 - 415 = (8m + b) - (5m + b)
249 = 3m
Dividing both sides by 3, we find:
m = 249 / 3
m = 83
Now, substituting the value of m into the first equation:
664 = 8(83) + b
664 = 664 + b
Therefore, b = 0.
The equation representing the relationship between x and y is:
y = 83x + 0
y = 83x
c. As the y-intercept (b) is 0, the equation does not have a constant term. This means that the relationship is "direct" or "proportional." The y-coordinate starts at 0, implying that when the x-coordinate (time) is 0, the distance traveled will also be 0.
To find the answers to these questions, we need to analyze the given table for x and y.
a. To determine the distance traveled per minute, we can calculate the average rate of change. We will divide the change in distance (y) by the change in time (x). Let's calculate the average rate of change for the given data pairs:
Average Rate of Change = (Change in Distance) / (Change in Time)
For the first two data pairs:
(415 - 664) / (5 - 8) = -249 / -3 = 83
For the next two data pairs:
(581 - 415) / (7 - 5) = 166 / 2 = 83
For the last two data pairs:
(747 - 581) / (9 - 2) = 166 / 7 = 23.71
Based on the calculations, for this dataset, every minute around 83 meters are traveled.
b. To write an equation to show the relationship between x and y, we need to determine the pattern or the equation representing the relationship. Let's plot the given data points on a graph to visualize the relationship between time (x) and distance traveled (y).
Using the given data, let's plot the points on a graph:
(x, y) points:
(8, 664)
(5, 415)
(7, 581)
(2, 166)
(9, 747)
Now, let's plot these points on a graph.
Once plotted, we can observe the pattern and find the equation representing the relationship between x and y.
However, without visualizing the graph, it is difficult to determine the exact equation.
c. Once we have the equation, we can determine the type of relationship by examining the form of the equation. Additionally, the y-intercept can provide insight into the relationship.
Since we don't have the equation yet, it is not possible to determine the type of relationship or the y-intercept from the given information.
To find the equation, you can use various methods depending on the pattern you observe in the plotted points, such as linear regression, quadratic regression, etc.