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)
looks good to me.
You are correct! Let's go through each description to determine whether it represents a linear function or not:
6. The price for x pounds of cheese at $6.99 per pound (LINEAR FUNCTION):
You are correct, this is a linear function. The description suggests a proportional relationship between the price and the weight of cheese. As the weight increases or decreases, the price will change linearly at a constant rate, $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 are correct, this is not a linear function. The description indicates a change in velocity over time, which does not follow a linear pattern. The acceleration and deceleration of the car would result in a curved or non-linear relationship.
8. A runner's heart rate while running on a treadmill with inclines increasing every 7 minutes (LINEAR FUNCTION):
You are correct, this is a linear function. The description explains that the incline on the treadmill increases at a regular interval of 7 minutes. As time increases, the runner's heart rate will change linearly since it is directly influenced by the treadmill's incline.
9. The price for y pounds of strawberries at $2.99 per pound (LINEAR FUNCTION):
You are correct, this is a linear function. Similar to the cheese example, this description presents a proportional relationship between the price and the weight of strawberries. The price changes linearly at a constant rate of $2.99 per pound.
10. The amount of money remaining on a movie gift card after renting one movie a week for 6 weeks (LINEAR FUNCTION):
You are correct, this is a linear function. The description indicates a consistent decrease (assuming the movies have a fixed cost) in the amount of money on the gift card over time. The decrease occurs at a constant rate since one movie is rented per week, resulting in a linear relationship between the number of weeks and the amount of money remaining on the gift card.
Well done! Your answers are correct for all the descriptions.