Writing an Equation to Represent a Proportional Relationship

An expression of equapty of ratios is called a proportion. The proportion expressing the equapty of the ratios A:B and C:D is written A:B = C:D or A:B::C:D. This form, when spoken or written, is often expressed as

A is to B as C is to D.

A, B, C and D are called the terms of the proportion. A and D are called the extremes, and B and C are called the means.

For example, from a table of equivalent ratios below, proportions can be written as follows 1:3::2:6 and 2:6::3:9

The proportional relationship can also be written as

$frac{y}{x} = frac{3}{1} = frac{6}{2} = frac{9}{3}$

An equation to represent the proportional relationship would be

$y = 3x$

Write an equation to represent the proportional relationship given in the table.

Solution

Step 1:

The proportional relationship can be written as

$frac{l}{k} = frac{7}{3} = frac{28}{12} = frac{35}{15}... = frac{7}{3}$

Step 2:

So, the equation representing this proportional relationship is $l = frac{7}{3} imes frac{k}{1} = frac{7k}{3}$

or $l = frac{7k}{3}$

Write an equation to represent the proportional relationship given in the table.

Solution

Step 1:

The proportional relationship can be written as

$frac{b}{a} = frac{15}{5} = frac{21}{7} = frac{24}{8}... = frac{3}{1}$

Step 2:

So, the equation representing this proportional relationship is $b = frac{3}{1} imes frac{a}{1} = frac{3a}{1} = 3a$

or $b = 3a$

Write an equation to represent the proportional relationship given in the table.

Solution

Step 1:

The proportional relationship can be written as

$frac{s}{r} = frac{6}{10} = frac{12}{20} = frac{18}{30}... = frac{3}{5}$

Step 2:

So, the equation representing this proportional relationship is $s = frac{3}{5} imes frac{r}{1} = frac{3r}{5}$

or $s = frac{3r}{5}$