Solve direct variation problems and find the constant of variation (k).
Last updated: March 2026 | By ForgeCalc Engineering
Step 1: Find Constant (k)
Step 2: Solve for New Y
Direct variation describes a simple relationship between two variables. We say $y$ varies directly with $x$ if the ratio between them is constant. This means that as one variable increases, the other increases at a consistent rate.
Graphically, direct variation is always represented by a straight line that passes through the origin (0,0). The slope of this line is the constant of variation, $k$.
Where $k$ is the constant of variation ($k \neq 0$).
Problem: If y varies directly as x, and y = 12 when x = 3, find y when x = 10.
Step 1: Find k
k = y / x = 12 / 3 = 4
Step 2: Write equation
y = 4x
Step 3: Solve for new x
y = 4 * 10 = 40
Final Answer: y = 40
In direct variation (y=kx), variables move in the same direction. In inverse variation (y=k/x), as one variable increases, the other decreases.
Yes. By definition, if x = 0, then y = k(0) = 0. If a line does not pass through the origin, it is not a direct variation.
Yes. If k is negative, y will decrease as x increases, but the relationship is still direct because the ratio y/x remains constant.
Divide each y-value by its corresponding x-value. If the result (k) is the same for every pair, it is a direct variation.
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