After 5 showings of a movie, a theater had earned a profit of $2,000. After 7 showings, the profit was $3,000. Assuming a linear function, write an equation in the form y=mx+b that shows the profit earned from showing the movie.

Step-by-step explanation:

Let x represent the number of showings of a movie.

Let y represent the amount earned from x showings.

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m = change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 - x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

From the information given,

y2 = 3000

y1 = 2000

x2 = 7

x1 = 5

Slope, m = (3000 - 2000) / (7 - 5) = 1000/2 = 500

To determine the intercept, we would substitute x = 5, y = 2000 and m = 500 into y = mx + c. It becomes

2000 = 500 * 5 + c = 2500 + c

c = 2000 - 2500 = - 500

The equation becomes

y = 500x - 500