Inverse Proportion: The Product Stays Fixed
When y = a/x, the product xy is the same at every point, so every rectangle drawn from a point on the curve to the axes has the same area, the curve is symmetric about the origin, and its lattice points are the factor pairs of a -- while points between the curve and the axes satisfy a product inequality instead. Meshed gears are the same law: teeth times turns is shared.
grade 7–8 FunctionsRatiosGeometry Draw a DiagramMake a Systematic List
Progression (4)
g8 1. Meshed gears share teeth times turns FunctionsRatios
g7 2. Equal xy at two points fixes the ratio GeometryExpressions
g7 3. Constant xy fixes the triangle's area Number systemGeometry
g7 4. Count one quadrant, then use point symmetry RatiosNumber system