Write direct variation equations

Learning Objectives Define direct variation and identify the constant of variation. Determine if a relationship between two variables represents a direct variation. Write a direct variation equation when given two corresponding values. Write a direct variation equation from a table of values. Write a direct variation equation from a real-world scenario. Use a direct variation equation to find an unknown value. Ever notice how the more songs you download, the more storage space you use? 📱 That's a direct variation in action! In this tutorial, you will learn how to recognize a special relationship called direct variation. We will focus on how to find the 'constant of variation' and use it to write a powerful equation that describes this relationship, allowing...

TermDefinitionExample Direct VariationA relationship between two variables, typically x and y, where as one variable increases, the other increases at a constant rate. Their ratio is always constant.If you earn $15 per hour, your total earnings (y) vary directly with the number of hours you work (x). The more hours you work, the more you earn. Constant of VariationThe non-zero constant ratio in a direct variation, represented by the variable 'k'. It's the 'rate' that connects the two variables.In the $15 per hour pay scenario, the constant of variation (k) is 15, because the ratio of earnings to hours (y/x) is always 15. Dependent VariableThe variable (usually y) whose value depends on the value of another variable.In `y = 3x`, the value of `y` depends on the valu...

The Direct Variation Equation y = kx This is the fundamental equation for any direct variation. 'y' and 'x' are the variables, and 'k' is the constant of variation. This equation shows that y is always a constant multiple of x. The Formula for the Constant of Variation k = y/x To find the constant of variation (k), divide any corresponding y-value by its x-value. This formula is derived by rearranging the main equation `y = kx`.