Could someone check my answer: the question is: The equation y= 12x +5 shows the total cost for
ordering tickets on the phone for a certain outdoor concert.
Tickets are $12 each, and there is a one-time service
fee of $5. Can the slope of this line be thought of as
a rate? Explain. I realize that it looks like it could be thought of as a rate but the definition of a rate states that it is ratio of two quantities that involve different units such as miles to gallons. So I am thinking that the slope would not be considered a rate because both numbers are the same unit (money)
no, it is a rate
think of the 12x as (12/1)x, that is,
it costs $12 per 1 ticket, so the 12 is the >b>rate of money per ticket, "two quantities that involve different units"
To check your answer, let's go through the equation and understand what each part represents.
In the given equation, y = 12x + 5, let's assign labels to different variables:
- y represents the total cost for ordering tickets on the phone for a certain outdoor concert.
- x represents the number of tickets ordered.
Now, let's consider the slope of the line, which is the coefficient of x, in this case, 12. The slope of a line can indeed be thought of as a rate.
In this scenario, the slope of 12 can be interpreted as the rate at which the total cost increases per ticket. For each additional ticket ordered, the total cost increases by $12. Therefore, the slope represents the rate of change in cost per ticket.
Even though the units for both numbers in this case are the same (money), the slope still represents a rate because it defines the change in the dependent variable (y) with respect to the independent variable (x). It indicates a consistent increase in the total cost for each additional ticket, regardless of the units involved.
Hence, the slope can be considered a rate, even when both numbers involve the same units.