Question

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?

Answer 1

p= 11.50 s

Explanation:

Answer 2

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