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3 years ago

Find the slope and the y- intercept of the line y=2x-6

Mathematics

1 answer:

Alchen [17]3 years ago

8 0

Answer:

The slope is 2 and the y-intercept is -6

Step-by-step explanation:

we know that

The equation of the line in slope intercept form is equal to

$y=mx+b$

where

m is unit rate or the slope of the linear equation

b is the y-intercept or initial value (value of y when the value of x is equal to zero)

In this problem we have

$y=2x-6$

therefore

the slope is equal to

$m=2$

and

$b=-6$

<u><em>Verify</em></u>

For x=0

$y=2(0)-6=-6$ ---> is ok

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3 years ago

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3 years ago

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3 years ago

A store has been selling 300 Blu-ray disc players a week at $600 each. A market survey indicates that for each $40 rebate offere

timurjin [86]

Answer:

75 $

Step-by-step explanation:

According to problem statement p(300) = 600

And we know that with a rebate of 40 $, numbers of units sold will increase by 80 then if x is number of units sold, the increase in units is

( x - 300 ) , and the price decrease

(1/80)*40 = 0,5

Then the demand function is:

D(x) = 600 - 0,5* ( x - 300 ) (1)

And revenue function is:

R(x) = x * (D(x) ⇒ R(x) = x* [ 600 - 0,5* ( x - 300 )]

R(x) = 600*x - 0,5*x * ( x - 300 )

R(x) = 600*x - 0,5*x² - 150*x

R(x) = 450*x - (1/2)*x²

Now taking derivatives on both sides of the equation we get

R´(x) = 450 - x

R´(x) = 0 ⇒ 450 - x = 0

x = 450 units

We can observe that for 0 < x < 450 R(x) > 0 then R(x) has a maximum for x = 450

Plugging this value in demand equation, we get the rebate for maximize revenue

D(450) = 600 - 0,5* ( x - 300 )

D(450) = 600 - 225 + 150

D(450) =

D(450) = 600 - 0,5*( 150)

D(450) = 600 - 75

D(450) = 525

And the rebate must be

600 - 525 = 75 $

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3 years ago