Final answer:
The correct linear function for the landscaping company that charges $46 per cubic yard plus a delivery fee of $20 is f(x) = 46x + 20, with $46 being the slope and $20 as the y-intercept.
Step-by-step explanation:
The question is asking to find the linear function for a landscaping company that charges a certain amount per cubic yard, with an additional delivery fee. This is a typical scenario where a linear function is used to model the total cost based on the number of cubic yards a customer purchases.
The company charges $46 per cubic yard and adds a delivery fee of $20. The variable 'x' in the function represents the number of cubic yards purchased. The cost is directly proportional to the number of cubic yards, hence the slope is the price per cubic yard ($46), and the y-intercept is the delivery fee ($20), which is the cost when x is 0.
Therefore, the correct linear function is:
f(x) = 46x + 20
Where 'x' is the number of cubic yards and 'f(x)' is the total cost.