The graph below shows the prices of different numbers of swimsuits at a store: a graph is shown. the values on the x axis are 0, 2, 4, 6, 8, and 10. the values on the y axis are 0, 23, 46, 69, 92, and 115. points are shown on ordered pairs 0, 0 and 2, 23 and 4, 46 and 6, 69 and 8, 92. these points are connected by a line. the label on the x axis is number of swimsuits. the title on the y axis is price in dollars. which equation can be used to determine p, the cost of s swimsuits?

The given data can be tabulated as:

Number of swimsuits, s (x)          Price, p (y)

0                                                              0

2                                                              23

4                                                              46

6                                                              69

8                                                              92

10                                                           115

We can see that by looking alone, the value of price p is increasing at a constant rate of 23 therefore the equation relating s and p must be linear in the form of:

y = m x + b

or

p = m s + b

where m is the slope of the line and b is the y intercept

The slope m can be calculated using the formula below and any two data points:

m = (y2 – y1) / (x2 – x1)

m = (23 – 0) / (2 – 0)

m = 11.5

The value of b (y-intercept) is the value of y when x = 0, therefore b = 0

The whole equation then becomes:

p = 11.5 s