Britany works at a call center for a home shopping network. The table below shows the number of orders placed with the network per day based on the number of calls received per day by the network.
Number of Calls, x 200 250 300 350 400
Number of Orders, N 172 227 274 328 376
Which equation best models this set of data?
A.
N = x - 25
B.
N = x2 - 25
C.
N = -x + 25
D.
N = -x2 + 25
To determine the best equation that models the data, we can create a linear regression to find the equation of the line of best fit. Let's first calculate the slope:
Slope = (N2 - N1) / (x2 - x1)
Slope = (227 - 172) / (250 - 200)
Slope = 55 / 50
Slope = 1.1
Now that we have the slope, we can use the point-slope form of a linear equation to find the y-intercept:
N = mx + b
172 = 1.1(200) + b
172 = 220 + b
b = -48
Therefore, the equation that models the data would be:
N = 1.1x - 48
So, the correct answer is not provided in the options.