Chapter 3:Ratio and Proportion, 3.2:Direct Proportion

What is direct proportion?

  • Two quantities are directly proportional when they increase or decrease in the same ratio.

  • If one quantity doubles, the other also doubles.

  • If one quantity is halved, the other is also halved.

Direct proportion equation

  • y ∝ x means y is directly proportional to x.

  • This can be written as y = kx.

  • k is called the constant of proportionality.

Constant of proportionality

  • The constant of proportionality is the value of y ÷ x.

  • For directly proportional quantities, y ÷ x always has the same value.

Using direct proportion

  • Find the constant of proportionality first.

  • Use the constant to find the unknown value.

  • The relationship must pass through the origin (0, 0) when shown on a graph.

Direct proportion graphs

  • A graph of two directly proportional quantities is a straight line.

  • The line passes through the origin.

  • A steeper line means a larger constant of proportionality.

Important

  • Direct proportion means the ratio between the two quantities stays constant.

  • If x increases by a certain factor, y increases by the same factor.

  • Direct proportion is different from simply having a straight-line relationship; the graph must pass through the origin.