y is inversely proportional to √x. When x = 4, y = 15. Find y when x = 25.
- Write the equation: y = k/√x.
- Find k: 15 = k/√4 = k/2, so k = 30.
- Use it: y = 30/√25 = 30/5 = 6.
Answer: y = 6
Direct and inverse proportion
Maths · Ratio, proportion and rates of change. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
The idea
Two quantities are in direct proportion when they change by the same factor: if one doubles, the other doubles. Their ratio stays the same, and the graph is a straight line through the origin.
Two quantities are in inverse proportion when one is multiplied and the other is divided by the same factor: if one doubles, the other halves. Their product stays the same, and the graph is a curve that falls and never touches the axes.
Harder questions use a power or a root, such as "y is proportional to x2". Write an equation with a constant k, use the given pair of values to find k, then use the equation.
Rules to remember
- y is directly proportional to x: y = kx, so y ÷ x is constant.
- y is inversely proportional to x: y = k/x, so x × y is constant.
- "Inversely proportional to x" means the same as "directly proportional to 1/x".
- Other forms: y = kx2, y = k√x, y = k/x2.
- If y is proportional to xn and x is multiplied by c, then y is multiplied by cn.
- Unitary method (direct): find the value for one item first, then multiply.
Common mistake
Treating an inverse proportion as a direct one. More workers take less time, so multiply workers by days to get the total work, then divide.
Worked example
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