A water park conducted a study to investigate the relationship between outdoor temperature and the number of park visitors. The correlating linear model is shown, where x represents the number of degrees over 70°F, and y represents the number of park visitors.

y = 42 + 15x

What is the correct interpretation of the y-intercept?

A.

When the temperature is 70°F, the park can expect 0 visitors.

B.

When the temperature is 70°F, the park can expect 42 visitors.

C.

When the temperature is 70°F, the park can expect 57 visitors.

D.

When the temperature is 70°F, the park can expect 15 visitors.

b) When the temperature is 70°F, the park can expect 42 visitors.

Step-by-step explanation:

Given that y represents the number of park visitors and x is the number of degrees over 70°F. The equation of the model is given as:

y = 42 + 15x

The general equation of a straight line plotted y against x with an intercept (c) on the y-axis and a slope (m) is given by the equation:

y = mx + c

comparing y = mx + c with y = 42 + 15x, the slope of the line y = 42 + 15x is 15 and its intercept on the y axis is 42.

This means that at temperature 70°F, x is 0.

therefore y = 42 + 15 (0) = 42

Therefore when the temperature is 70°F, the park can expect 42 visitors.