4. 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 83 meters are traveled. b. Write an equation to show the relationship between x and y: y = 83x . c. This relationship is proportional because the y-intercept is .

Answer 1

To determine if the relationship is proportional, we need to analyze the equation \( y = 83x \).

1. The equation \( y = 83x \) indicates a direct relationship between distance (y) and time (x), where 83 represents the constant rate of travel in meters per minute.

2. A relationship is considered proportional if it can be expressed in the form \( y = kx \), where \( k \) is a constant and there is no y-intercept (the line passes through the origin (0,0)).

3. Since the equation is \( y = 83x \), it indeed shows a direct proportionality between \( x \) and \( y \) because:

• The y-intercept is 0.
• This means when \( x = 0\), \( y\) would also be \( 0\), which indicates that at zero time, there is zero distance traveled.

Thus, the final part c can be completed as follows:

c. This relationship is proportional because the y-intercept is 0.