Question

If 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

Answer 1

The linear equation for attendance is y = 11550 – 725x.

Step-by-step explanation:

Given:

Price of admission=$14

Attendance for a week=1400 customers

Amount dropped is admissions price=$12

Attendance increased after price reduction= 2850 per week

Solution:

We have to write a linear equation for the attendance

Now, consider two points (14, 1400) and (12, 2850)

such that x – axis represents price of admission and y – axis represents attendance.

So, we have to find line equation of the above two points.

We know that, general equation of a line passing through two points (x1, y1), (x2, y2) in point slope form is given by

`((y-y_1))/((y_2-y_1))=((x_2-x_1))/((x- x_))`

`(y-y_1) = (y_2-y_1)((x_2-x_1))/((x- x_1))`…………………………….(1)

Substituting the values in (1)

`y -1400 = ((2850-1400))/((12-14))(x -14)`

`y- 1400 = (1450)/(-2)(x-14)`

y – 1400 = -725(x – 14)

y = 1400 – 725x + 725 x 14

y = 1400 – 725x + 10150

y = 11550 – 725x