To address the given questions based on the provided data, we can start by analyzing the relationship between time (x) and distance (y).
a. Every minute
To determine the distance traveled per minute, we can calculate the average distance traveled per minute based on the given data:
- Total distance traveled (sum of y): \(40 + 25 + 35 + 10 + 45 = 155\) meters.
- Total time (sum of x): \(8 + 5 + 7 + 2 + 9 = 31\) minutes.
Average distance per minute = Total distance / Total time = \(155 , \text{meters} / 31 , \text{minutes} \approx 5 , \text{meters}\).
Response: 5
b. Write an equation to show the relationship between x and y.
To find the equation relating x and y, we can analyze the pairs given:
Using the slope formula \( m = \frac{\Delta y}{\Delta x} \):
- For specific pairs, we can choose (2, 10) and (9, 45): \[ m = \frac{45 - 10}{9 - 2} = \frac{35}{7} = 5 \text{ meters per minute.} \] The equation of the line in slope-intercept form is \(y = mx + b\). Here \(m = 5\).
Now we have to find \(b\) (the y-intercept). We can use a point; for (2, 10): \[ 10 = 5(2) + b \implies 10 = 10 + b \implies b = 0. \]
Response: \(y = 5x\)
c. The relationship is
The relationship we have is a linear relationship, as represented by the equation we derived.
Response: linear
because the y-intercept is
The y-intercept we found is 0.
Response: 0
So the final completed inputs would be:
- a: 5
- b: y = 5x
- c: linear
- because the y-intercept is: 0
3 answers