Section 1
Variables on the Coordinate Plane
Property
For the function y = f(x),
x is the independent variable because it is plotted on the horizontal x-axis and represents the input.
y is the dependent variable because it is plotted on the vertical y-axis and its value depends on x.
Examples
- The total cost, C, of buying g gallons of gas at 3 dollars per gallon is C = 3g. The number of gallons g is the independent variable (x-axis), and the total cost C is the dependent variable (y-axis).
- The number of hours of daylight, D, changes based on the day of the year, t. The day t is the independent variable, and the hours of daylight D is the dependent variable.
- The distance a car travels, d, after h hours at a constant speed of 60 mph is given by d = 60h. The time h is the independent variable, and the distance d is the dependent variable.
Explanation
The independent variable is the input, or the value you control and choose. It always goes on the bottom horizontal line (x-axis) of a graph. The dependent variable is the output, because its value depends on whatever input you selected. It goes on the side vertical line (y-axis). Think of it as cause (x-axis) and effect (y-axis).