Question

In a graph, x represents the number of months since a business opened, and y represents the total amount of money the business has earned. The following three points are from the graph:

(2, 1990) (5, 4225) (9, 7205)

Find the slope and y-intercept. Explain what each represents.

Answer 1

Use first two points and the slope equation to find the slope:

• m = (4225 - 1990)/(5 - 2) = 745

The slope is 745.

Use the first point and point-slope equation to find the y-intercept:

• y - y₁ = m(x - x₁), where m- slope, (x₁, y₁) - the given point

• y - 1990 = 745(x - 2)
• y - 1990 = 745x - 1490
• y = 745x - 1490 + 1990
• y = 745x + 500

The y-intercept is 500.

The slope of 745 represents the profit per month and the y-intercept of 500 represents the initial profit.