Question

1. the table shows the heights (in feet) of the waves at a beach and the numbers of surfers at the beach.

wave height	3	6	5	1	4
number of surfers	24	61	56	15	35

surfing

a) plot the data from the table on the graph.
b) describe the relationship between the two data sets.
c) how many surfers might be at the beach if the waves were 2 feet high?

Explanation:

Step1: Plot the data points

On the graph, for wave - height 3, plot the point (3, 24); for wave - height 6, plot (6, 61); for wave - height 5, plot (5, 56); for wave - height 1, plot (1, 15); for wave - height 4, plot (4, 35).

Step2: Analyze the relationship

As the wave - height increases, the number of surfers generally increases. So, there is a positive correlation between wave - height and the number of surfers.

Step3: Estimate the number of surfers for wave - height 2

We can use linear interpolation. The points (1, 15) and (3, 24) are closest to a wave - height of 2. The slope between (1, 15) and (3, 24) is $m=\frac{24 - 15}{3 - 1}=\frac{9}{2}=4.5$. Using the point - slope form $y - y_1=m(x - x_1)$ with the point (1, 15) and $x = 2$, we have $y-15 = 4.5\times(2 - 1)$, so $y=15 + 4.5=19.5\approx20$.

Answer:

a) Plot the points (3, 24), (6, 61), (5, 56), (1, 15), (4, 35) on the given graph.
b) There is a positive correlation between wave - height and the number of surfers.
c) Approximately 20 surfers.