Sure, let's break down the responses one by one based on the data given.
a. Every minute Response area meters are traveled.
To calculate how many meters are traveled per minute, we can find the average distance per minute. The total distance traveled (sum of y values) is \(40 + 25 + 35 + 10 + 45 = 155\) meters, and the total time spent (sum of x values) is \(8 + 5 + 7 + 2 + 9 = 31\) minutes. Thus, the average distance per minute is given by:
\[ \text{Average distance per minute} = \frac{155 \text{ meters}}{31 \text{ minutes}} = 5 \text{ meters per minute} \]
Thus, the response for (a) is: Response area: 5
b. Write an equation to show the relationship between x and y.
From analyzing the data, we can see the relationship between distance and time appears to be linear. Considering the average slope of distance over time (which represents how distance varies with time), we use the slope we just computed:
The relationship of distance y to time x can be described as: \[ y = 5x \]
So for (b), the response is: Response area: y = 5x
c. The relationship is Response area because the y-intercept is Response area.
Since we have established that the relationship is linear (as derived from the equation \(y = 5x\)), we can analyze the y-intercept, which occurs when \(x = 0\).
The equation \(y = 5x\) has a y-intercept of 0 because it crosses the y-axis at (0,0). Therefore:
For (c), the relationship is: Response area: proportional
And because the y-intercept is: Response area: 0
To summarize:
- (a): 5
- (b): y = 5x
- (c): proportional; 0