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The Pool Fun Company has learned​ that, by pricing a newly released Fun Noodle at $ 2 comma sales will reach 9000 Fun Noodles per day during the summer. Raising the price to $ 5 will cause the sales to fall to 6000 Fun Noodles per day.

a.  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).

The Pool Fun Company has learned that by pricing a newly released Fun Noodle at 2 comma sales will reach 9000 Fun Noodles per day during the summer Raising the class=

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AwesomeLegends77

Answer:

x[9000] x y[2] > x[5000] x y[5]

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The slope-intercept form of the equation representing the relation between sales price and number sold is given as:

[tex]y = -1000x + 11000[/tex]

Given that:

  • x represents sales price in dollars.
  • y represents numbers of Fun Noodles sold
  • When x = $2, y = 9000 packets.
  • When x = $5, y = 6000 packets.
  • The relation between x and y is linear.

To find:

Slope intercept form of the equation representing relation between sales price and numbers of items sold.

Formation of equation:

Since it is assumed that there is linear relation between x and y, thus, let the equation be:

[tex]y = mx + c[/tex] , where m represents the slope of the line and c represents the intercept on y axis  of the linear line that this equation is representing.

Then, we have that line passing through two points, viz:

[tex](2, 9000)[/tex] and [tex](5, 6000)[/tex]

Since as the price increases from 2 to 5 (ie growth of 3 in value of x), the numbers of items sold decreases from 9000 to 6000 (that means downfall of 3000 in value of y)

Thus, we have rate as:   x up by 3 implies y down by 3000

Which can be converted to find the slope as:

[tex]\: \rm slope = m = \dfrac{\text{difference in y}}{\text{difference in x}} = \dfrac{-3000}{3} = -1000[/tex]

Thus, the equation will be:

[tex]y = -1000x + c[/tex]

Evaluating the equation at (2, 9000) to get the value of c:

[tex]y = -1000x + c\\9000 = -1000 \times 2 + c\\9000 + 2000 = c\\c = 11000[/tex]

Thus, the equation of the line representing the relation between sales price and the numbers of Fun Noodles sold will be:

[tex]y = -1000x + 11000[/tex]

Learn more about linear equations here:

https://brainly.com/question/14362668

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