Write a linear equation for the attendance in terms of the price, p. ( A=mp+b )

Question

A local cinema found that if the price of admission was $14, the attendance was about 1400 customers per week. When the price of admission was dropped to $12, attendance increased to about 2850 per week. Write a linear equation for the attendance in terms of the price, p. ( A=mp+b )

Answer 1

Write a linear equation for the attendance in terms of the price, p. ( A=mp+b )A local cinema found that if the price of admission was $14, the attendance was about 1400 customers per week. When the price of admission was dropped to $12, attendance increased to about 2850 per week. Write a linear equation for the attendance in terms of the price, p. ( A=mp+b)

 

in order to find the equation you need the slope and the y intercept

 

if you plot the two points (price ,Attendance),

($14,1400 customers/week), and ($12,2850 customers/week) on a Cartesian systems of coordinates, you will get a straight line whose slope is m=y2-y1/x2-x1 This is the point slope form equation, substituting for the terms:

 

m=(2850-1400/12-14)=1450/-2= -725

 

taking any point say (14,1400) and the slope m

 

-725=(y-1400)/(x-14) solving

 

-725(x-14)=y-1400, -725x+10150=y-1400, add +1400 to both sides

 

-725x+10150+1400=y, y= -725x+11550 is your equation of the line where 11550 is the y intercept when x = 0