Direct Proportion
Direct proportion means two quantities are linked so they change together in exactly the same way. When one goes up, the other goes up by the same factor - when one goes down, the other follows suit.
The key insight is that when you divide the values, you always get the same number. This magic number is called the constant of proportionality (represented by k), and it's what makes the whole relationship work.
You can write any direct proportion relationship using the equation y = kx, where k is your constant. This simple formula is your go-to tool for solving proportion problems.
Here's how to tackle a typical question: if y is directly proportional to x, and when x = 3, y = 7.5, find y when x = 4.4. First, find k by substituting: 7.5 = k × 3, so k = 2.5. Then use y = 2.5x with x = 4.4 to get y = 11.
Quick Check: In direct proportion, if one value doubles, the other value doubles too - the relationship stays perfectly consistent!