Variation · 1.2.2
Finding k in inverse variation
This standard builds on inverse variation by asking you to actually determine 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 = k/x. With this equation, you can then calculate any missing value of x or y.
The official learning standard (1.2.2)
“Determine the relation between two variables for an inverse variation.”
What it means
This standard builds on inverse variation by asking you to actually determine 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 = k/x. With this equation, you can then calculate any missing value of x or y.
How it is examined
In Paper 1, a table or a single pair of values may be given for you to find k, or an unknown value, directly. In Paper 2, finding the relation y = k/x is usually the first step of a structured question, leading into further calculations or a real-life application.
Worked example
y varies inversely as x. When x = 4, y = 9.
Determine the relation between y and x, and hence find the value of y when x = 6.
- Since y varies inversely as x, write y = k/x.
- Substitute x = 4, y = 9: 9 = k/4, so k = 36.
- The relation is y = 36/x.
- When x = 6: y = 36/6 = 6.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What if I'm given a graph of y against 1/x instead of y against x?
Since y = k/x can be rewritten as y = k(1/x), a graph of y against 1/x is actually a straight line through the origin, with gradient k. So you can find k the same way you would for a direct variation graph.
Can two different pairs of x and y give different values of k?
No, if the relationship truly is inverse variation, multiplying x and y together must give the same k for every pair of matching values. If two pairs give different products, the relationship is not a pure inverse variation.
How do I check that my equation y = k/x is correct?
Substitute your original given values of x and y back into your equation. If both sides balance correctly, your value of k and your equation are correct; if they do not match, recheck your working for the value of k.