The equation y=12x+5 shows the total coat for ordering tickets on the phone for a certain outdoor concert. if the tickets are $12 each, & there is a one time service fee of $5, can the slope of this line be thought of as a rate??
Please explain this.
the equation y=12x+5
has the same form as y = mx + 5
where m is the slope or the rate.
Slope is defined as (change of y)/(change of x)
In your case, the cost changes $12 per ticket, that is, a rate of $12/1 ticket
Yes, the slope of the line y = 12x + 5 can be thought of as a rate. In this context, the equation represents the total cost (y) for ordering tickets on the phone as a function of the number of tickets purchased (x). The slope of the line, which is 12 in this case, indicates the rate at which the total cost increases with each additional ticket.
To better understand this, let's break down the equation. The term "12x" represents the cost of each ticket multiplied by the number of tickets purchased. Since the tickets are $12 each, the cost for x tickets would be 12 times x, which gives us 12x.
The term "+ 5" represents the one-time service fee of $5. This fee is constant and does not change based on the number of tickets purchased. Therefore, it is added to the cost of the tickets.
By looking at the slope, 12, we can see that for each additional ticket purchased, the total cost increases by $12. This shows the rate at which the cost is changing with respect to the number of tickets.
In summary, the slope of the line y = 12x + 5 represents the rate of increase in the total cost of ordering tickets for the concert. Each unit increase in the number of tickets results in a $12 increase in the total cost.