   SEARCH HOME Math Central Quandaries & Queries  Question from lavada, a student: i need the definition to dependent variable The dependent variable is the one whose value depends on another variable or variables (the independent variables).

For example, consider throwing a ball straight up with a speed of v. Let h be the maximum height the ball goes. How high will it go? That depends on the speed that you chose to throw the ball. So h depends on v. This means v is the independent variable (you choose it) and h is the dependent variable (it depends on h). The equation, by the way, would be h = v2/19.6, assuming you measure height in meters and speed in meters per second.

When we draw graphs, we put the dependent variable on the vertical axis. So you usually choose the value along the horizontal axis and determine the value along the vertical value.

Mostly, we write line equations in the form y = mx + b (which is called "slope-intercept" form) in order to graph them. This lets us choose a value for x, and calculate the value for y. So we make the x values the horizontal (independent) values and the y values the vertical (dependent) axis.

If we were doing a science experiment and measuring the growth of a population of bacteria in a dish, then we are choosing "when" to do the counting, so time is the independent choice, and it is graphed along the horizontal axis. The population is dependent on time and is graphed along the vertical axis. Since these are measurements, we don't have a formula, but the principle still applies: the dependent variable is something you determine and the independent variable is something you choose or decide upon.

Hope this helps,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.