# Linear Relationships

**Episode #8 of the course Everyday math by Jenn Schilling**

Welcome to Lesson 8! Today, we will discuss linear relationships, which describes the behavior of two different variables when they vary in proportion to one another.

**The Math**

Let’s start with a few definitions. A variable in math is usually represented by a symbol, such as *x* or *y*. A variable represents something unknown or something that can change depending on different factors. For example, variables are often used to represent lines or curves on a graph, and the equation of the line tells us how *y* changes based on *x*. Variables in an experiment or study represent the different factors of the study that are either controlled or changed. There are three different types of variables in an experiment. The dependent variable is the observed variable that is measured. The independent variable is the variable that is changed or manipulated. The controlled variable is held constant or kept the same.

Proportionality is another important term in linear relationships. Two variables are proportional if there is a constant ratio between them. Proportional relationships between two variables can be represented by a straight line on a graph (the slope is constant).

So, linear relationships are interactions between variables that are proportional, meaning that as one variable changes, the other also changes at a constant rate. Linear relationships appear in statistics when considering the correlation between variables, which tells us how close the relationship is between two different variables in a trial or experiment.

**Everyday Applications**

Linear relationships also occur in many everyday places. For example, any time you want to make a conversion between different types of measurement—say, inches to centimeters or cups to liters—you use a linear relationship, because you multiple one measurement by a constant number to turn it into the other measurement.

Any time we consider rates, we are using linear relationships. For example, the time it takes to travel a certain distance depends on the speed at which you travel. Speed limit enforcement is often done using radar, which measures the distance traveled over a certain period of time; the speed of the vehicle can then be determined by dividing distance by time.

Understanding proportionality is also useful when evaluating experiments and consuming news stories about scientific studies. Often, relationships between variables are presented without proper explanations, which can make the conclusions challenging to understand. However, with this new knowledge of proportionality and variables (along with the statistics coming up in Lesson 10), you will now be able to evaluate basic experiments for their validity. Did the experiment include control variables? Is the relationship between the independent variable and the dependent variable truly linear and proportional? Now you can successfully interpret these questions!

Tomorrow, we will dive into probability before turning to statistics! See you then!

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