Direct and inverse proportion – table and graph
MathematicsAlgebraAges 12–13
Use it with your class: students open it from a link or a QR code, with no account needed.
Next in Algebra
A table of values and the graph of y = kx (direct proportion) or y = k/x (inverse proportion). Drag the point on the graph horizontally to change x and watch y change with it; drag vertically to change the constant k. The table below shows the ratio y/x (always equal to k) or the product x·y (always equal to k), helping students spot the signature of each type of relationship.
Lesson: Direct proportion; inverse proportion
What it shows
Direct and inverse proportion are shown side by side as a formula, a table of values and a graph. In direct proportion, y = kx: the ratio y/x is constant, multiplying x by a factor multiplies y by the same factor, and the graph is a straight line through the origin. In inverse proportion, y = k/x: the product x·y is constant, multiplying x by a factor divides y by it, and the graph is a curve (a hyperbola) that never meets the axes. The table shows that y falling as x rises does not make a relationship inverse.
How to use
Choose Direct proportion y = kx, drag the red point sideways to change x and up or down to change k, and check the ratio y/x in the table. Switch to Inverse proportion y = k/x and compare the product x·y. Raise the upper end in Domain of x, from 1 to so students see more of each graph. Ask them to predict y after doubling or tripling x before moving the point.
Parameters you can change
- Constant of proportionality k 0.5–24
- Relationship type Direct proportion y = kx, Inverse proportion y = k/x
- Domain of x, from 1 to 4–20
- Show table of values
Questions to explore
- Is y = 10 − x an inverse proportion, and what does the table of values show?
- When x is multiplied by 3, how does y change in direct proportion and in inverse proportion?
- If y = 6 when x = 4, what is k for a direct proportion and for an inverse proportion?
