Answer to Question #134470 in Algebra for js

Question #134470
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.
1
Expert's answer
2020-09-30T20:00:11-0400

We know that,


Slope=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)

(x1,y1)(x_1, y_1) (x2,y2)(x_2, y_2)

is.


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


Slope(m)=(y2y1)/(x2x1)Slope (m) =(y_2-y_1)/(x_2-x_1)


Slope(m)=(11,0009,000)/(8085)Slope(m) =(11,000-9,000)/(80-85)


Slope(m)=400Slope(m)=-400


Therefore

yy1=m(xx1)y-y_1=m(x-x_1)

m=400m=-400

y1=9,000y_1=9,000

x1=85x_1=85


(y9,000)=400(x85)(y-9,000)=-400(x-85)

y9,000=400x+34,000y-9,000=-400x+34,000


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

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


2.

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

y=400×65+43,000y=-400×65+43,000

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

y=17,000y=17,000




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