Question

Write an equation that expresses the statement.

y is proportional to x and inversely proportional to t.

Short answer

Equation that represents the statement is $\mathrm{yt}=\mathrm{ks}$.

Step-by-step solution

Step 1. Understanding Direct variation.

Direct Variation is said to be the relationship between two variables in which one is a constant multiple of the other.

For example:

$\mathrm{y}=\mathrm{kx}$

Here width="35">k≠0, y is directly proportional to x and vice versa.

Step 2. Understanding inverse proportion.

The relation between two variables is inversely proportional when,

$\mathrm{y}=\frac{\mathrm{k}}{\mathrm{x}}$or $\mathrm{xy}=\mathrm{k}$

Here $\mathrm{k}\ne 0$, y is inversely proportional to x and vice versa.

Step 3. Write the final equation that expresses the statement.

Final equation is:

$\begin{array}{l}\mathrm{y}=\mathrm{k}\left(\frac{\mathrm{s}}{\mathrm{t}}\right)\\ \mathrm{yt}=\mathrm{ks}\end{array}$