Respuesta :
Answer:
a. Compare the y-intercepts and rates of changes.
Remember that in the form [tex]y=mx+b[/tex], the coeffiecient of the variable is the rate of change, and the constant is the y-intercept.
In this case, we have the equation
[tex]p=5b-15[/tex]
Where [tex]p[/tex] is the profit and [tex]b[/tex] 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)
[tex]r=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\\ r=\frac{15-5}{3-1}=\frac{10}{2}\\ r=5[/tex]
The are of Kate's profist is 5 dollars per bracelet.
Now we use the point-slope formula
[tex]y-y_{1} =m(x-x_{1} )\\y-5=5(x-1)\\y=5x-5+5\\y=5x[/tex]
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.
b. How much will each girl make if she sells 30 bracelets.
Carol would make
[tex]p=5b-15=5(30)-15\\p=135[/tex]
$135 profit.
Kate would make
[tex]y=5x=5(30)=150[/tex]
$150 profit.
So, Kate would make $15 more than Carol.
