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# Direct proportion

Two variables $\Tblue{a}$ and $\Tgreen{b}$ are proportional, or in direct proportion, if the ratio $\Tblue{a}/\Tgreen{b}$ is constant for all values of the variables.

At constant speed, distance covered is proportional to time.

We write $\Tblue{a}\,\Torange{\propto}\,\Tgreen{b}$ using the proportionality symbol $\Torange{\propto}$.

The ratio $\Tred{k}$ between proportional variables is the proportionality constant. $\Tblue{a}=\Tred{k}\,\Tgreen{b},\qquad \Tblue{a}:\Tgreen{b} = 1:\Tred{k}.$

Several variables are collected in the table below. The variables $\Tblue{a}$ and $\Tgreen{b}$ are proportional with proportionality constant $\Tred{3}$. The variables $\Tblue{a}$ and $\Tgreen{c}$ are not proportional.

 Variable Variable Ratio Variable Ratio $\Tblue{a}$ $\Tblue{3}$ $\Tblue{6}$ $\Tblue{9}$ $\Tblue{12}$ $\Tblue{15}$ $\Tgreen{b}$ $\Tgreen{1}$ $\Tgreen{2}$ $\Tgreen{3}$ $\Tgreen{4}$ $\Tgreen{5}$ $\Tred{a/b}$ $\Tred{3}$ $\Tred{3}$ $\Tred{3}$ $\Tred{3}$ $\Tred{3}$ $\Tgreen{c}$ $\Tgreen{3}$ $\Tgreen{12}$ $\Tgreen{27}$ $\Tgreen{48}$ $\Tgreen{75}$ $\Tred{a/c}$ $\Tred{1}$ $\Tred{0.5}$ $\Tred{0.33}$ $\Tred{0.25}$ $\Tred{0.2}$
The price paid is directly proportional to the weight of the fruit. The proportionality constant depends on the units used to weigh the fruit.