Direct & Inverse Variation

When numbers change together in a consistent way, we call this variation. Direct variation happens when two values increase or decrease together at the same rate. This relationship is written as y = kx, where k is called the constant of variation (also known as proportionality). This constant equals the slope of the line formed when the relationship is graphed.

Imagine earning $15 per hour - your pay directly varies with the hours worked. More hours always means more money, following the same pattern.

Inverse variation works differently. When one value goes up, the other goes down, following the equation y = k/x. Notice how x appears in the denominator (bottom) of the fraction. This creates a curved line when graphed rather than a straight one.

Remember this: In direct variation, as x increases, y increases. In inverse variation, as x increases, y decreases. Look at where x appears in the equation - on top $y = kx$ means direct, on bottom $y = k/x$ means inverse.

Think of inverse variation like this: if it takes 4 workers 6 hours to complete a job, 8 workers could finish it in 3 hours. More workers means less time - an inverse relationship.