Question

Given the table for x, time in minutes and y, distance traveled in meters:
x - time (minutes) | 8 | 5 | 7 | 2 | 9
y - distance (meters) | 40 | 25 | 35 | 10 | 45
a. Every minute _____________ meters are traveled.
b. Write an equation to show the relationship between x and y. _____________
c. The relationship is ____________ because the y-intercept is _____________
Options: proportional, non proportional, non linear, -5, 5, 40, -40, y = x/5, 5y = x, y = x - 5, y = 5x, y = 40x, 40y = x, (5, 25), (0, 5), (0, 0), (5, 0)

Answer 1

To analyze the given information:

### a. Every minute _____________ meters are traveled.
To determine the distance traveled per minute, we can look at the relationship between time (x) and distance (y). To calculate the average speed, we can use the pairs of (x, y):

1. For (5 minutes, 25 meters): \( \frac{25}{5} = 5 \) meters per minute
2. For (2 minutes, 10 meters): \( \frac{10}{2} = 5 \) meters per minute
3. For (7 minutes, 35 meters): \( \frac{35}{7} = 5 \) meters per minute
4. For (8 minutes, 40 meters): \( \frac{40}{8} = 5 \) meters per minute
5. For (9 minutes, 45 meters): \( \frac{45}{9} = 5 \) meters per minute

Thus, every minute **5 meters** are traveled.

### b. Write an equation to show the relationship between x and y. _____________
From our calculations, the relationship can be expressed as:
\[ y = 5x \]

### c. The relationship is ____________ because the y-intercept is _____________
1. The relationship is **proportional** because for each value of x, there is a consistent linear relationship with y (i.e., the ratio of distance to time is constant).
2. The y-intercept is **0**, since when \( x = 0 \), \( y = 0 \).

Thus, we have:

- a. Every minute **5** meters are traveled.
- b. Write an equation to show the relationship between x and y. **y = 5x**
- c. The relationship is **proportional** because the y-intercept is **(0, 0)**.