Variation · 1.0.2
Finding k in direct variation
This standard builds on direct variation by asking you to actually work out the relation: given one pair of matching values (or a table or graph), you find the constant of variation k, then write the equation y = kx. Once you have this equation, you can calculate any missing value of x or y.
The official learning standard (1.0.2)
“Determine the relation between two variables for a direct variation.”
What it means
This standard builds on direct variation by asking you to actually work out the relation: given one pair of matching values (or a table or graph), you find the constant of variation k, then write the equation y = kx. Once you have this equation, you can calculate any missing value of x or y.
How it is examined
In Paper 1, a table or a pair of values may be given for you to find k or an unknown value directly. In Paper 2, finding the relation y = kx is usually the first step of a structured question, which then leads to further calculations or a real-life application.
Worked example
y varies directly as x. When x = 5, y = 15.
Determine the relation between y and x, and hence find the value of y when x = 12.
- Since y varies directly as x, write y = kx.
- Substitute x = 5, y = 15: 15 = k(5), so k = 3.
- The relation is y = 3x.
- When x = 12: y = 3(12) = 36.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
How do I find k if I'm given a graph instead of a value pair?
Since y = kx can be seen as a straight line through the origin, k is simply the gradient of that line. Pick any clear point (x, y) on the graph, other than the origin, and calculate k = y ÷ x, or use rise over run instead.
Can two different given pairs of x and y give different values of k?
No, not if the relationship really is direct variation. Every pair of matching x and y values must give the same value when you divide y by x.
If two pairs give different k values, the relationship is not a pure direct variation.
What if x = 0 is one of the given values, does the equation still work?
Yes. Direct variation y = kx naturally gives y = 0 when x = 0, since the line passes through the origin.
This is a useful check: a table or graph that does not pass through (0, 0) is not showing direct variation.