Carol's profit at a craft fair is represented by the function p = 5b - 15, where p is the profit and b is the number of bracelets she sells. kate's profit in shown in the table. bracelets sold (x) 1 2 3 4 profit (in dollars) (y) a. compare the y-intercepts and rates of change. b. how much will each girl make if she sells 30 bracelets?

Remember that in the form , the coeffiecient of the variable is the rate of change, and the constant is the y-intercept.

In this case, we have the equation

Where is the profit and is the number of bracelets. Her rate of change is $5 per bracelet and its y-intercept is at -15.

On the other hand, the table below represents Kate's profits

Bracelets sold (x)    Profit (in dollars) (y)

         1                                 5

         2                                10

         3                                15

         4                                20

First, we need to find the rate using the following formula and two pairs of the table (1,5) and (3,15)

The are of Kate's profist is 5 dollars per bracelet.

Now we use the point-slope formula

This means the y-intercept is at zero.

If we compare, we would deduct that Carol's profit begins with -$15, while Kate's profit begins at $0, in other words, Carol has a debt. Also, both of them have the same rate of profit $5 per bracelet.

Carol would make

$135 profit.

Kate would make

$150 profit.

So, Kate would make $15 more than Carol.

AC is greater than BC because segment AC is the hypotenuse of right triangle ABC, and the hypotenuse is the longest side of a right triangle.