Direct Variation
Direct Variation is a core Grade 8 math concept taught in Saxon Math, Course 3. It describes a proportional relationship between two variables where y = kx, and k is the constant of variation. Students learn to identify, write, and graph direct variation equations.
Key Concepts
New Concept Direct variation describes a relationship where two quantities increase or decrease together at a constant rate. When two variables are proportional, the value of one variable can be found by multiplying the other by a constant factor. We call this relationship between the variables direct variation . $$y = kx$$ In this equation, $x$ and $y$ are the variables, and $k$ is the constant multiplier, called the constant of proportionality . What’s next Now that you have the basics, you'll learn to identify direct variation from tables and graphs and solve problems using the constant of proportionality.
Common Questions
What is direct variation in math?
Direct variation is a relationship between two variables where one is a constant multiple of the other, expressed as y = kx, where k is the constant of variation.
How do you find the constant of variation?
Divide y by x: k = y/x. If this ratio is the same for all pairs in the table, the relationship is a direct variation.
What is the difference between direct variation and a linear equation?
A direct variation always passes through the origin (0,0), while a general linear equation may have a y-intercept other than zero.
How do you graph a direct variation?
Plot the origin (0,0) and use the slope k to find additional points. The graph is always a straight line through the origin.
Where does direct variation appear in real life?
Examples include distance = speed × time, total cost = price per item × number of items, and other proportional real-world relationships.