Constant of variation
Find the constant of variation k in Grade 9 algebra using k=y/x from any point on a direct variation y=kx, then apply k to write the equation and predict unknown values.
Key Concepts
Property The letter $k$ represents the constant of variation . In an inverse relationship, you can always find it using the formula $k=xy$. Explanation The constant of variation, $k$, is the secret code of the relationship! It's the one number that never changes, representing the fixed product of $x$ and $y$. If you can find $k$ by multiplying any known $(x, y)$ pair, you unlock the ability to write the master equation and solve for any other value in the relationship. Examples If $y$ varies inversely with $x$, and $y=5$ when $x=4$, the constant of variation is $k = (4)(5) = 20$. To write an inverse variation equation where $y=2$ when $x=9$, first find $k$. $k = (9)(2)=18$. The equation is $y = \frac{18}{x}$.
Common Questions
What is the constant of variation?
In a direct variation y = kx, the constant of variation k is the fixed ratio between y and x for all points on the graph. It describes how fast y changes relative to x and is found by computing k = y ÷ x.
How do you find the constant of variation from a table or ordered pairs?
Divide the y-value by the x-value for any pair (avoiding (0,0)). If all ratios are equal, that value is k. For the pair (4, 12): k = 12/4 = 3, so the equation is y = 3x.
What does a larger constant of variation mean graphically?
A larger k means a steeper line through the origin. For k = 5, the line rises faster than for k = 2. A negative k produces a line that decreases as x increases. k directly equals the slope of the direct variation line.