Question

What is the constant of proportionality \[k\]?

Answer 1

Hint: From the given question we have been asked to explain the constant of proportionality. Generally the constant of proportionality is the ratio of two values or quantities. The constant of proportionality is different for the direct variation and for indirect variation. So, we will explain the definitions of the direct variation and the indirect variation and then we will find the value of the constant of proportionality for these two and explain it briefly. So, the solution will be as follows.

Complete step-by-step solution:
Direct Variation:
If \[y\] is directly proportional to \[x\], then we can write as follows.
\[\Rightarrow y=kx\]
Where \[k\] is the constant of proportionality.
If you solve for \[k\], we get the value of it as follows.
\[\Rightarrow k=\dfrac{y}{x}\]
We have the ratio of \[y\] and \[x\].
Hence, the constant of proportionality is the ratio between two quantities that are directly proportional.
Inverse Variation:
If \[y\] is inversely proportional to \[x\], then we can write the equation as follows.
\[\Rightarrow y=\dfrac{k}{x}\]
where \[k\] is the constant of proportionality.
If you solve for \[k\], we get the value of \[k\] as follows.
\[\Rightarrow k=xy\]
we have, which is the product of \[y\] and \[x\].
Hence, the constant of proportionality is the product of quantities that are inversely proportional.

Note: Students should have good knowledge in the concept of variation especially the direct and indirect variation and its properties. In the direct variation as \[y\] is directly proportional to \[x\] we should not think that the constant of proportionality is product of two quantities as the constant of proportionality will be \[\Rightarrow k=\dfrac{y}{x}\] which is the ratio of quantities.