To find the answers to your questions, we can analyze the given data for time (x) and distance (y).
Given values:
- \(x\) (time in minutes): 8, 5, 7, 2, 9
- \(y\) (distance in meters): 40, 25, 35, 10, 45
a. Every minute [_] meters are traveled.
To find the average rate of distance traveled per minute, we can calculate the total distance traveled and divide it by the total time taken.
Total distance: \(40 + 25 + 35 + 10 + 45 = 155\) meters
Total time: \(8 + 5 + 7 + 2 + 9 = 31\) minutes
Average rate: \[ \text{Average rate} = \frac{\text{Total distance}}{\text{Total time}} = \frac{155}{31} \approx 5 \text{ meters per minute} \]
So, we can fill in the blank:
a. Every minute [5] meters are traveled.
b. Write an equation to show the relationship between x and y.
To find the relationship between time (x) and distance (y), let's assume a linear relationship of the form:
\[ y = mx + b \]
Where \(m\) is the slope (distance per minute) and \(b\) is the y-intercept.
From our calculation above, we found that the average distance per minute (slope \(m\)) is approximately 5. To find the y-intercept (\(b\)), we can choose a pair of data points; let's use the first point (8, 40).
Using the equation: \[ y = mx + b \] We can plug in \(y = 40\), \(m = 5\), and \(x = 8\):
\[ 40 = 5(8) + b \ 40 = 40 + b \ b = 0 \]
Thus, the relationship can be expressed as: \[ y = 5x + 0 \ \text{or simply} \ y = 5x \]
So we fill in the blank:
b. Write an equation to show the relationship between x and y. [y = 5x]
c. The relationship is [] because the y-intercept is [].
We have determined that the relationship is linear because we have established a linear equation in the format \(y = mx + b\) with a constant slope.
Since \(b\) (the y-intercept) is 0, we can fill in the blanks:
c. The relationship is [linear] because the y-intercept is [0].