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2 years ago

What is an equation in point slope form of the line that passes through (7, 1) and (-3,9)

Mathematics

1 answer:

LuckyWell [14K]2 years ago

5 0

Answer:

y= -4/5x+33/5

Step-by-step explanation:

for questions like these, the slope is always defined as the change in y over the change in x or use the equation m=y2-y1/x2-x1.

x1=7 and y1=1

x2=-3 and y2=9

now plug these numbers in to the equation. m= 9-1 / -3-7 Or m= 8/-10 simplified to m= -4/5

now that we have the slope you can plug it in to the equation y=mx+b and get y= -4/5 + b.

to find b, the y-intercept, you can use either of the two points and the answer will be the same. for this one, I'll use (7,1).

1= -4/5 x 7+b. b= 33/5

HOPE THIS HELPS!!

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2 years ago

A restaurant operator in Accra has found out that during the lockdown,if she sells a plate of her food for Ghc 20 each,she can s

ella [17]

The demand equation illustrates the price of an item and how it relates to the demand of the item.

The slope of the demand function is -1/2
The equation of the demand function is: $R(x) = (300 - 10x) \times (20 + 5x)$
The price that maximizes her revenue is: Ghc 85

From the question, we have:

$Plates = 300$

$Price = 20$

The number of plates (x) decreases by 10, while the price (y) increases by 5. The table of value is:

$\begin{array}{cccccc}x & {300} & {290} & {280} & {270} & {260} \ \\ y & {20} & {25} & {30} & {35} & {40} \ \end{array}$

The slope (m) is calculated using:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

So, we have:

$m = \frac{25-20}{290-300}$

$m = \frac{5}{-10}$

$m = -\frac{1}{2}$

The equation of the demand is as follows:

The initial number of plates (300) decreases by 10 is represented as: (300 - 10x).

Similarly, the initial price (20) increases by 5 is represented as: (20 + 5x).

So, the demand equation is:

$R(x) = (300 - 10x) \times (20 + 5x)$

Open the brackets to calculate the maximum revenue

$R(x) =6000 + 1500x - 200x - 50x^2$

$R(x) =6000 + 1300x - 50x^2$

Equate to 0

$6000 + 1300x - 50x^2 =0$

Differentiate with respect to x

$1300 - 100x =0$

Collect like terms

$100x =1300$

Divide by 100

$x =13$

So, the price at maximum revenue is:

$Price= 20 + 5x$

$Price= 20 + 5 * 13$

$Price= 85$

In conclusion:

The slope of the demand function is -1/2
The equation of the demand function is: $R(x) = (300 - 10x) \times (20 + 5x)$
The price that maximizes her revenue is: Ghc 85