Question

The Pool Fun Company has learned​ that, by pricing a newly released Fun Noodle at $4, sales will reach 8000 Fun Noodles per day during the summer. Raising the price to $5 will cause the sales to fall to 6000 Fun Noodles per day.

Assume that the relationship between sales​ price, x, and number of Fun Noodles​ sold, ​ y, is linear. Write an equation in​ slope-intercept form describing this relationship. Use ordered pairs of the form​ (sales price, number​ sold).

type your answer in slope intercept
b. predict the daily sales of Fun Noodles if the price is $4.50​

Answer 1

The equation that describes the relationship between the sales price and number of Fun Noodles sold is y = -2000x + 16000. If the price is $4.50, it is predicted that the daily sales of Fun Noodles would be approximately 11000.

Step-by-step explanation:

The equation that describes the relationship between the sales price, x, and the number of Fun Noodles sold, y, is

y = mx + b, where m is the slope and b is the y-intercept. In this case, we have two points: (4, 8000) and (5, 6000).

Using these points, we can calculate the slope by dividing the change in y by the change in x: (6000-8000)/(5-4) = -2000.

Now that we have the slope, we can substitute one of the points into the equation to solve for the y-intercept. Let's use the point (4, 8000): 8000 = -2000(4) + b.

Simplifying this equation, we find that b = 16000.

Now we can write the equation in slope-intercept form: y = -2000x + 16000.

To predict the daily sales of Fun Noodles if the price is $4.50, we substitute x = 4.50 into the equation: y = -2000(4.50) + 16000.

Evaluating this equation, we find that y ≈ 11000.

Therefore, the predicted daily sales of Fun Noodles would be approximately 11000 if the price is $4.50.

Answer 2

Answer: PART A:

The generic equation of the line is:

y-yo = m (x-xo)

First we look for the slope of the line:

m = (y2-y1) / (x2-x1)

m = ((5000) - (6000)) / (4-3)

m = -1000

Then, we substitute any point in the generic equation:

(xo, yo) = (4, 5000)

Substituting:

y-5000 = (- 1000) (x-4)

Rewriting:

y = -1000x + 4000 + 5000

y = -1000x + 9000

The equation is:

y = -1000x + 9000

PART B:

For the price of 3.50 we have:

y = -1000 * (3.5) +9000

y = 5500

Step-by-step explanation: