Write a linear equation

Question

A local aquarium found that if the price of admission was $15 , the attendance was about customers 950 per week. When the price of admission was dropped to $8 , attendance increased to about 2250 per week. Write a linear equation for the attendance in terms of the price, p.

( A = mp + b )

Answer 1

You could graph the relation, plot 2 points, (15,950) and (8, 2250) Then use the point slope form of a linear equation.

It illustrates the downward sloping demand curve, where quantity purchased increases as price decreases.

The slope = m = rise/run = change in y value divided by change in x value. 950 to 2250 is a 1300 increase. The change in x value is negative 7. The slope is -1300/7

The equation is y=mx+b

y=-1300x/7 + b

plug in either point to calculate b

950 = -1300(15)/7 + b

b = 950 + 19500/7 = 6650/7 +19500/7 = 26150/7

y=(-1300/7)x + 26150/7

A = (-1300/7)p + 26150/7

Attendance = about 3736 - 186 times price

If price were zero, if admission were free, a little less than 4,000 would attend.

if price were $20, no one would come. That's roughly the x and y intercepts

For every one dollar increase in price, about 200 less people attend