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The Pool Fun Company has learned that, by pricing a newly released Fun Noodle at $3, sales will reach 6000 Fun Noodles per day during the summer. Raising the price to $4 will cause the sales to fall to 5000 Fun Noodles per day.

a. Assume the 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 pars of the form (sales price, number sold).

The equation is?

b. Predict the daily sales of Fun Noodles if the price is $3.50.

? sales

? sales

Respuesta :

carlosego
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
ernikhil

(a) The equation in slope-intercept form  for describing the relationship between sales price and quantity of the fun noodle is [tex]y=-1000x+9000[/tex].

(b) The daily sales of fun noodles is [tex]5500[/tex] when, the sales price is [tex]\$3.50[/tex].

(a) The general slope-intercept form of writing the equation of a line is [tex]y-y_1=m(x-x_1)[/tex] where, [tex]m[/tex] is the slope of the line.

According to the question,

[tex](x_1,y_1)\rightarrow (3,6000)[/tex] and [tex](x_2,y_2)\rightarrow (4,5000)[/tex]

Evaluate the value of the slope as-

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}\\m=\dfrac{5000-6000}{4-3}\\m=-1000[/tex]

Now, substitute the parameters in the equation [tex]y-y_1=m(x-x_1)[/tex]-

[tex]y-y_1=m(x-x_1)\\y-6000=-1000(x-3)\\y-6000=-1000x+3000\\y=-1000x+9000[/tex]

Hence, the equation in slope-intercept form  for describing the relationship between sales price and quantity of the fun noodle is [tex]y=-1000x+9000[/tex].

(b) Substitute [tex]x=\$3.50[/tex] in the slope-intercept equation  [tex]y=-1000x+9000[/tex] to evaluate the daily sales of fun noodles as-

[tex]y=-1000x+9000\\y=-1000(3.50)+9000\\y=-3500+9000\\y=5500[/tex]

Hence, the daily sales of fun noodles is [tex]5500[/tex] when, the sales price is [tex]\$3.50[/tex].

Learn more about slope-intercept form here:

https://brainly.com/question/20786109?referrer=searchResults

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