Example 1. Suppose it is girl scout cookie season. :) You have committed to buy ten boxes of cookies from your own daughter, and also to buy three boxes from every other girl scout that comes to your door selling cookies. The total amount of cookies you buy does not depend on how many boxes you buy from each girl, but on the number of girls that come to your door. Therefore, the cookies you buy from your own daughter can be considered fixed, and the cookies from other girl scouts can be considered variable. If your total cookie purchase (in boxes) is expressed as y, and the number of girl scouts you buy cookies from is expressed as x, then y = 10 + 3x.
- Solving the x-intercept for y = 10 + 3x (y = 0)
0 = 10 + 3x
-10 = 3x
-(10/3) = x
-3.33 = x
x-intercept is (-3.33, 0) - Solving the y-intercept for y = 10 + 3x (x = 0)
y = 10 + 3*0
y = 10 + 0
y = 10
y-intercept is (0, 10)
- Solving the x-intercept for y = 2*5 + 20x (y = 0)
0 = 2*5 + 20x
0 = 10 + 20x
-10 = 20x
-(10/20) = x
-0.5 = x
x-intercept is (-0.5, 0) - Solving the y-intercept for y = 2*5 + 20x (x = 0)
y = 2*5 + 20*0
y = 10 + 0
y = 10
y-intercept is (0, 10)
- Solving the x-intercept for y = 2(31-x) + 4x (y = 0)
0 = 2(31-x) + 4x
0 = 2*31 - 2x + 4x
0 = 62 + 2x
-62 = 2x
-(62/2) = x
-31 = x
x-intercept is (-31, 0) - Solving the y-intercept for y = 2(31-x) + 4x (x = 0)
y = 2(31-0) + 4*0
y = 2*31 + 0
y = 62
y-intercept is (0, 62)