Determine the number of customers each shop has on days 10 and 20. Use this information to write the function modeling the number of customers at the second shop.
y=2.5x+30
Practice makes perfect
We are asked to find a linear function that models the number of customers at the second shop. We will start by determining the number of customer each shop has on days 10 and 20. Next, we will use this information to write the equation of the linear function.
How many customers does each shop have on days 10 and 20?
We are given a function that models the daily number of customers y at the first coffee shop, depending on the number of days x since the beginning of the month.
y=0.25x^2-5x+80
Since both shops have the same number of customers on days 10 and 20, we will use the given function rule to determine the number of customers each shop has on these days. Let's start with day 10!
On day 10 each shop has 55 customers. Therefore, the point (10,55) is included in the graph of the linear function modeling the number of customers at the second shop. Let's follow the same process for day 20!
On day 20 each shop has 80 customers. The point (20,80) is another point included in the graph of the linear function.
What function models the number of customers at the second shop?
We know two points included in the graph of the linear function modeling the number of customers at the second shop.
(10,55) and (20,80)
Recall that exactly one line passes through any two points. Therefore, using these points, we are able to write an equation of the line modeling the number of customers at the second shop. Let's write the equation of the line in slope-intercept form.
y=mx+b
Here m is the slope and b is the y-intercept. Let's use the Slope Formula to find the slope m of the line passing through ( 10,55) and (20,80).
