Question

Question A family is going from Dallas, Texas, to Los Angeles, California. They have traveled 500 miles so far. The next day, their average speed is 70 miles per hour. Write an equation for the distance they traveled, y , and the hours they have driven, x . Indicate whether this is a proportional or a nonproportional situation.(1 point)

Answer 1

To model the situation, we need to find an equation that relates the distance traveled \( y \) to the hours driven \( x \) after they have already traveled 500 miles.

Since their average speed for the next part of the trip is 70 miles per hour, we can express the relationship as follows:

\[
y = 500 + 70x
\]

Here, \( y \) represents the total distance traveled (in miles), and \( x \) represents the hours driven after they have already traveled 500 miles.

### Proportional vs. Nonproportional

1. **Proportional Situation**: In a proportional relationship, the equation can be expressed in the form \( y = kx \), where \( k \) is a constant, and the graph of the equation passes through the origin (0,0).

2. **Nonproportional Situation**: If the equation has a y-intercept other than zero, it is a nonproportional relationship.

In our case, the equation \( y = 500 + 70x \) has a y-intercept of 500 (i.e., when \( x = 0 \), \( y = 500 \)). Therefore, this indicates that they have already traveled 500 miles before considering the additional distance traveled.

Thus, this situation is **nonproportional** because it does not pass through the origin and has a constant term (the 500 miles already traveled).