Patrick wanted to gather data about the cost of joining a community pool in his area. he plotted the data and determined that the average community pool membership cost consists of a one-time registration fee and a monthly fee modeled by the equation y = 15x + 40.
identify and interpret the y-intercept in this model.
a. the y-intercept is 15. this is the cost of registration.
b. the y-intercept is 15. this is the cost per month.
c. the y-intercept is 40. this is the cost per month.
d. the y-intercept is 40. this is the cost of registration.

Option d

The y-intercept is 40. This is the cost of registration.

Step-by-step explanation:

Note that in this problem we have 2 variables:

x: number of months

y: average community pool membership cost

The linear equation that models the equation is:

Note that the equation is increasing, that is, as x increases, the variable y increases as well.

To find the interception of the line with the axis and we must do x = 0

This means that the minimum value that the variable y can take is

In other words represents the minimum cost, that is, the registration cost.

The answer is the option d.

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step-by-step explanation:

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c