Question

A local movie theater found that if the price of admission was $15, the attendance was about

1,150 customers per week. when the price of admission was dropped to $8, the attendance increased to about
2,050 per week. Write a linear equation for the attendance in terms of the price
p: a=mp+b.

Answer 1

To determine the equation representing attendance in terms of price, we calculate the slope from the two given points and apply the y-intercept formula. The final linear equation is a = (-900/7)p + (27750/7).

Step-by-step explanation:

The student is asking for a linear equation a=mp+b to represent the attendance (a) in terms of the price of admission (p). To create this equation, we need to calculate the slope (m) and y-intercept (b). With two given points, (15, 1150) and (8, 2050), we can determine the slope by taking the difference in attendance and dividing it by the difference in price:

Slope (m) = (Change in attendance) / (Change in price)
= (2050 - 1150) / (8 - 15)

We find that the slope m is -900/7. To find the y-intercept (b), we use one of the points and the slope in the point-slope formula, y - y1 = m(x - x1), where (x1, y1) is one of the given points.

The final linear equation representing attendance (a) in terms of the price (p) is:

a = (-900/7)p + b

Substitute point (15, 1150) to solve for b:

1150 = (-900/7)*15 + b

b = 1150 + (900/7)*15

After calculation, the y-intercept b is found to be 27750/7. Therefore, the complete linear equation is:

a = (-900/7)p + (27750/7)

This equation can now be used to predict attendance at different price points at this local movie theater.