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)
8 is probably not linear with time, nor slope, but I suspect your teacher wants you to say linear.
others ok.
6. The price for x pounds of cheese at $6.99 per pound (LINEAR FUNCTION):
To determine if this represents a linear function, we need to consider if the relationship between the pounds of cheese (x) and the price is a constant rate of change. In this case, the price increases by $6.99 for each pound of cheese. Since the rate of change is constant, this verbal description represents a 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):
In this scenario, the car's speed is changing, indicating a non-constant rate of change. Linear functions have a constant rate of change, so this verbal description does not represent a linear function.
8. A runner's heart rate while running on a treadmill with inclines increasing every 7 minutes (LINEAR FUNCTION):
To determine if this is a linear function, we need to consider whether the relationship between time and heart rate has a constant rate of change. Since the inclines are increasing every 7 minutes, the rate of change in the heart rate may not be constant. Therefore, this verbal description may not represent a linear function.
9. The price for y pounds of strawberries at $2.99 per pound (LINEAR FUNCTION):
Similar to example 6, this verbal description describes a situation with a constant rate of change. The price increases by $2.99 for each additional pound of strawberries, indicating a linear relationship between the weight and the price.
10. The amount of money remaining on a movie gift card after renting one movie a week for 6 weeks (LINEAR FUNCTION):
In this case, the amount of money remaining on the gift card is decreasing linearly as weeks pass by. Each week, the amount of money decreases by the same amount (the price of renting one movie). Therefore, this verbal description represents a linear function.