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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

1 answer

To determine the correct equation and whether the situation is proportional or nonproportional, we need to analyze the information given:

  • The family has already traveled 500 miles.
  • The next day, they will travel at an average speed of 70 miles per hour.

The total distance they travel (y) after driving for x hours on the next day can be modeled in the following way:

  1. The distance traveled on the next day at 70 mph would be \( 70x \).
  2. Adding the initial 500 miles gives us the total distance: \[ y = 70x + 500 \]

Now, regarding whether this is a proportional or nonproportional situation:

  • A proportional relationship would pass through the origin (0,0) and would mean that y is directly proportional to x.
  • A nonproportional relationship includes a constant added or subtracted, meaning it does not go through the origin.

Since the equation \( y = 70x + 500 \) includes the additional 500 miles (the initial distance traveled), it is a nonproportional situation.

Thus, the correct equation is: \[ y = 70x + 500, \text{ nonproportional} \]