Answer to Question #134470 in Algebra for js

Question

A manufacturer of graphing calculators has determined that 9,000 calculators per week will be sold at a price of $85 per calculator. At a price of $80, it is estimated that 11,000 calculators will be sold.

1. Determine a linear function that predicts the number of calculators that will be sold per week at a price of x dollars.

y = ____

2. Use this model to predict the number of calculators that will be sold at a price of $65.

Answer 1

We know that,

$Slope=$ change in y/change in x

If we represent number of calculators sold on y and decrease cost of calculators on the x axis.

So, the slope of line passing through the points (85, 9000) and ( 80, 11000)

$(x_1, y_1)$ $(x_2, y_2)$

is.

$Slope=$ change in number of calculator sold$\div$ decrease in the cost of calculator

$Slope (m) =(y_2-y_1)/(x_2-x_1)$

$Slope(m) =(11,000-9,000)/(80-85)$

$Slope(m)=-400$

Therefore

$y-y_1=m(x-x_1)$

$m=-400$

$y_1=9,000$

$x_1=85$

$(y-9,000)=-400(x-85)$

$y-9,000=-400x+34,000$

$$y=-400x+43,000$$

Hence, the linear function the perdicts the number of calculators per week is given by $y=-400x+43,000$

2.

The number of calculators that will be sold at a price of $65.

$y=-400×65+43,000$

$y=-26,000+43,000$

$y=17,000$