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 which equation best models the data, we can first look at the relationship between the number of calls and the number of orders.
Looking at the table, we can see that as the number of calls increases, the number of orders also increases. This suggests a positive correlation between the two variables.
A linear relationship between the number of calls and the number of orders can be modeled with a linear equation in the form y = mx + b, where y represents the number of orders, x represents the number of calls, m is the slope of the line, and b is the y-intercept.
To find the equation that best models the data, we can calculate the slope using two points from the table.
Using the points (200, 172) and (400, 376):
m = (376 - 172) / (400 - 200)
m = 204 / 200
m = 1.02
Now that we have the slope, we can find the y-intercept (b) by substituting the slope and one of the points into the equation and solving for b.
Using the point (200, 172):
172 = 1.02(200) + b
172 = 204 + b
b = 172 - 204
b = -32
So, the equation that best models the data is N = 1.02x - 32.
Therefore, the correct equation is not one of the options listed.