Hobbies: A book club charges a membership fee of $20 and then $12 for each book purchased.

a. Write and graph a function to represent the cost y of membership in the club based on the number of books purchased x.
b. what if...? Write and graph a second function to represent the cost of membership if the club raises its membership to $30.
c. Describe the relationship between your graphs from parts a and b.

a. y = 12x + 20

Cannot graph here.

b. y = 12x + 30

a. To write a function to represent the cost y of membership in the club based on the number of books purchased x, we need to consider two components: the initial membership fee and the additional cost per book.

The initial membership fee is $20, and for each book purchased, there is an additional cost of $12. Therefore, the function can be written as:
y = 20 + 12x

To graph this function, you can plot a set of points where x represents the number of books purchased, and y represents the cost of membership. Choose different values for x and evaluate the y-coordinates using the function. Then, plot these points on a coordinate plane and connect them to visualize the graph.

b. If the club raises its membership fee to $30, the new function representing the cost of membership would be:
y = 30 + 12x

Similarly, you can plot the points, where x represents the number of books purchased, and y represents the cost of membership. Evaluate the y-coordinates using the new function, plot the points, and connect them to create the graph.

c. The relationship between the graphs from parts a and b is that they have the same slope (12). However, they differ in their y-intercepts. In part a, the y-intercept is 20, representing the $20 initial membership fee. In part b, the y-intercept is 30, corresponding to the increased membership fee of $30. This means that the cost of membership increased by $10, but the additional cost per book remained the same.