Some useful types of variables are listed below. You will probably also have variables that you hold constant (control variables) in order to focus on your experimental treatment. You need to know which types of variables you are working with in order to choose appropriate statistical tests and interpret the results of your study. In statistical research, a variable is defined as an attribute of an object of study. Choosing which variables to measure is central to good experimental design.

Similarly, if one quantity decreases then the other quantity also decreases. Direct variation is a linear relationship hence, the graph will be a straight line. In a direct variation equation you have two variables, usually ??? When two quantities are related by a proportion, we say they are proportional to each other. Another way to express this relation is to talk about the variation of the two quantities. We will discuss direct variation and inverse variation in this section.

## Examples of Direct Variable Costs in a sentence

The force needed to break a board varies inversely with its length. Richard uses 24 pounds of pressure to break a 2-foot long board. The number of hours it takes for ice to melt varies inversely with the air temperature. Suppose a block of ice melts in 2 hours when the temperature is 65 degrees.

- Unlike direct costs, variable costs depend on the company’s production volume.
- The maximum load a beam will support varies directly with the square of the diagonal of the beam’s cross-section.
- The formula for the direction variation for a set of two quantities that are linearly dependent is as follows.
- Although direct and variable costs are tied to the production of goods and services, they can have some distinct differences.
- The relationship between the two quantities, y, and x is as follows.
- The cost of electricity is an indirect cost since it can’t be tied back to the product or the specific machine.

Furthermore, the ratio between x and y remains constant, as y is always 4 times x. This is what is meant when someone says that x and y are in direct variation, y varies directly with x, or y is directly proportional to x; they all mean the same thing. Two quantities as said to follow a direct variation if both increase or decrease by the same factor. Thus, an increase in one quantity leads to an increase in the other while a decrease in one quantity leads to a decrease in the other. In other words, if the ratio of the first quantity to the second quantity is a constant term, then the quantities are said to be directly proportional to each other. This constant value is known as the coefficient or constant of proportionality.

If you increase x, the value of y decreases. For example, if you move more quickly to your destination, your journey time will decrease. In this example, x is your speed and y is the journey time.

## Direct Relationships

In everyday life, we usually talk about miles/gallon. The number of gallons of gas Eunice’s car uses varies directly with the number of miles she drives. Last week she drove 469.8 miles and used 14.5 gallons of gas. Now we’ll solve a few applications of direct variation. Quantitative variables are any variables where the data represent amounts (e.g. height, weight, or age). The formula for the direction variation for a set of two quantities that are linearly dependent is as follows.

When Raoul runs on the treadmill at the gym, the number of calories, c, he burns varies directly with the number of minutes, m, he uses the treadmill. He burned 315 calories when he used the treadmill for 18 minutes. Our goal is to make science relevant and fun for everyone. Whether you need help solving quadratic equations, inspiration for the upcoming science fair or the latest update on a major storm, Sciencing is here to help.

## How to Tell if an Equation is a Direct Variation?

For example, how does the height that a ball bounces (y) depend on how high it’s dropped from (x)? By convention, x is the independent variable and y is the dependent variable. When there is a direct or inverse relationship, x and y are proportional to each other in some way. In direct relationships, an increase in x leads to a correspondingly sized increase in y, and a decrease has the opposite effect. In inverse relationships, increasing x leads to a corresponding decrease in y, and a decrease in x leads to an increase in y.

One example of direct variation is the speed of a car and the distance covered by it. If the speed increases the distance traveled within a certain time will also increase. Similarly, if the speed of the car decreases the distance covered within that interval of time will also decrease. When one quantity directly varies with respect to another quantity it is known as direct variation. This implies that if one quantity increases or decreases the other quantity also increases or decreases proportionately. It is the relationship between two variables where one of the variables is a constant multiple of the other.

Conversely, when one variable decreases, the other variable also decreases by the same factor. As such, the ratio between two variables that are in direct variation (or directly proportional) always remains the same. We solve inverse variation problems in the same way we solved direct variation problems. Only the general form of the equation has changed. We will copy the procedure box here and just change ‘direct’ to ‘inverse’.

## Difference Between Proportional & Linear Relationships

As you start to increase x, y decreases really quickly, but as you continue increasing x the rate of decrease of y gets slower. There are many examples of variables in the real world that are in direct variation, such as the gallons of gasoline pumped into a car, and the cost of the gasoline. The more gasoline that is pumped into the car, the higher the cost; the less gasoline pumped, the lower the cost. The rate at which a plant grows is another example. Direct variation refers to a relationship between two variables where when one variable increases the other also increases by the same factor.