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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) Responses y=70x , proportional y equals 70 x , proportional y=70x+500 , nonproportional y equals 70 x plus 500 , nonproportional y=500x+70 , nonproportional y equals 500 x plus 70 , nonproportional y=70x+500 , proportional y equals 70 x plus 500 , proportional

1 answer

To model the situation described, we can start by identifying the two components involved in the distance traveled: the distance already traveled (500 miles) and the additional distance they travel after that at a certain speed.

  1. Initial Distance Traveled: The family has already traveled 500 miles.
  2. Additional Distance Traveled: The next day, they will travel at an average speed of 70 miles per hour.

Let:

  • \( y \) be the total distance traveled after \( x \) hours of driving the next day.
  • The additional distance traveled can be modeled as \( 70x \).

Thus, the equation for the total distance \( y \) can be expressed as:

\[ y = 70x + 500 \]

This equation reflects the fact that they are adding the distance previously traveled (500 miles) to the distance they will travel at 70 miles per hour for \( x \) hours.

Proportional vs Nonproportional:

  • Proportional: In a proportional relationship, the equation would pass through the origin (0,0) and take the form \( y = kx \), where \( k \) is a constant (slope).
  • Nonproportional: In a nonproportional relationship, there is an initial value (y-intercept) at \( x = 0 \) that is not zero.

Since the equation \( y = 70x + 500 \) has a y-intercept of 500 (meaning when \( x = 0 \), \( y = 500 \)), this is a nonproportional situation.

Conclusion:

The correct choice is: \[ y = 70x + 500, \text{ nonproportional} \]