What is the equation of the line that has a slope of 4 and goes through the point (2, 8)
1 answer:
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A. Total Revenue (R) is equal to price per dive (P) multiplied by number of customers (C). We can write .
Per price increase is $20. So four price increase is $. Hence, price per dive is 100+80=$180.
Also per price increase, 2 customers are reduced from 30. For 4 price increases, customers are reduced. Hence, total customers is
.
So Total Revenue is:
B. Each price increase is 20. So x price increase is 20x. Hence, new price per dive would be equal to the sum of 100 and 20x.
Also per price increase, customers decrease by 2. So per x price increases, the customer decrease is 2x. Hence, new number of customers is the difference of 30 and 2x.
Therefor we can write the quadratic equation for total revenue as the new price times the new number of customers.
C. We are looking for the point (x) at which the equation modeled in part (B) gives a maximum value of revenue (y). That x value is given as , where a is the coefficient of
and b is the coefficient of x. So we have,
That means, the greatest revenue is achieved after 5 price increases. Each price increase was 20, so 5 price increase would be . So the price that gives the greatest revenue is
.
ANSWERS:
A. $3960
B.
C. $200
Answer:
4x +y = 3
Step-by-step explanation:
Perpendicular lines have slopes that are the negative reciprocals of one another. When the equation of the line is written in standard form like this, the equation of the perpendicular line can be written by swapping the x- and y-coefficients and negating one of them. Doing this much would give you ...
4x +y = (constant)
Note that we have chosen to make the equation read 4x+y, not -4x-y. The reason is that "standard form" requires the leading coefficient to be positive.
Now, you just need to make sure the constant is appropriate for the point you want the line to go through. So, it needs to be ...
4(2) +(-5) = constant = 3
The line of interest has equation ...
4x + y = 3
