Question

How do you find the constant of proportionality from the equation $ y = 7 \times 5x $ ?

Answer 1

Hint: In the given question, we are required to find the constant of proportionality for the relation between the variables x and y, $ y = 7 \times 5x $ . The constant value relating amounts that rise or fall uniformly together is called constant of proportionality. It can also be interpreted as the ratio of the amounts y and x.

Complete step by step solution:
So, we have to find the constant of proportionality for the equation $ y = 7 \times 5x $ .
In mathematics, two varying quantities are said to be in a relation of proportionality when they are multiplicatively connected to a constant which means that when either their ratio or their product yields a constant, the two physical quantities are said to be in proportionality relation. The value of the constant is called the coefficient of proportionality or the proportionality constant.
So, we have, $ y = 7 \times 5x $
Shifting x from right side of the equation to left side of the equation using transposition rule, we get,
 $ \Rightarrow \left( {\dfrac{y}{x}} \right) = 7 \times 5 $
Now, simplifying the calculations, we get,
 $ \Rightarrow \left( {\dfrac{y}{x}} \right) = 35 $
Hence, the proportionality constant for the equation $ y = 7 \times 5x $ is $ 35 $ .

Note: We should take care while doing the calculative steps. Definitions of proportions and constant of proportionality should be clear in one’s mind in order to solve such questions. We should also keep in mind the method used in solving the given problem as the same can be used for more such questions as well.