Determine whether each verbal description represents a linear function or not. Correct me if I'm wrong on any of these!!
6.The price for x pounds of cheese at $6.99 per pound (LINEAR FUNCTION)
7. A car accelerating on the highway to reach a speed of 62 mph then slowing down for a traffic jam. (NOT A LINEAR FUNCTION)
8. A runners heart rate while running on a treadmill with inclines increasing every 7 minutes. (LINEAR FUNCTION)
9.The price for y pounds of strawberries at $2.99 per pound (LINEAR FUNCTION)
10. The amount of money remaining on a movie gift card after renting one movie a week for 6 weeks (LINEAR FUNCTION)
6. The price for x pounds of cheese at $6.99 per pound (LINEAR FUNCTION)
- Correct! This is a linear function because the price increases or decreases proportionally with the number of pounds of cheese.
7. A car accelerating on the highway to reach a speed of 62 mph then slowing down for a traffic jam. (NOT A LINEAR FUNCTION)
- Correct! This is not a linear function because the speed of the car is not changing at a constant rate.
8. A runner's heart rate while running on a treadmill with inclines increasing every 7 minutes. (LINEAR FUNCTION)
- Incorrect. This is not a linear function because the heart rate does not increase or decrease at a constant rate. The inclines increasing every 7 minutes imply that the heart rate will likely change non-linearly.
9. The price for y pounds of strawberries at $2.99 per pound (LINEAR FUNCTION)
- Correct! This is a linear function because the price increases or decreases proportionally with the number of pounds of strawberries.
10. The amount of money remaining on a movie gift card after renting one movie a week for 6 weeks (LINEAR FUNCTION)
- Correct! This is a linear function because the amount of money remaining on the gift card decreases at a constant rate with each movie rental.
Great job! You got most of them correct. Let me clarify:
6. The price for x pounds of cheese at $6.99 per pound (LINEAR FUNCTION)
You're correct! The description represents a linear function because the price for a specific amount of cheese is directly proportional to the weight of the cheese. As the weight of the cheese increases, the price will also increase at a constant rate of $6.99 per pound.
7. A car accelerating on the highway to reach a speed of 62 mph then slowing down for a traffic jam (NOT A LINEAR FUNCTION)
You're absolutely right! This description does not represent a linear function. When a car accelerates, its speed increases at a non-constant rate until it reaches the desired speed. After that, when it slows down due to a traffic jam, the speed decreases. So the relationship between time and speed is not a straight line, making it not a linear function.
8. A runner's heart rate while running on a treadmill with inclines increasing every 7 minutes (LINEAR FUNCTION)
Here, your answer is incorrect. A runner's heart rate in this situation would not be a linear function. The heart rate is influenced by changes in incline, which do not occur at a constant rate. As the treadmill inclines increase, the heart rate will not change linearly. Therefore, the relationship between time and heart rate is not linear.
9. The price for y pounds of strawberries at $2.99 per pound (LINEAR FUNCTION)
Yes, you are correct! The description represents a linear function. The price for y pounds of strawberries is directly proportional to the weight of the strawberries. The price per pound remains constant at $2.99, so the relationship between weight and price is linear.
10. The amount of money remaining on a movie gift card after renting one movie a week for 6 weeks (LINEAR FUNCTION)
Absolutely correct! The description represents a linear function. The amount of money remaining on the gift card decreases by a fixed amount each week due to renting one movie. Since it decreases at a constant rate, the relationship between the number of weeks and the remaining balance is linear.
Well done on your answers! Remember, a linear function has a constant rate of change, resulting in a straight line when represented as a graph.