Question

Write an equation that expresses the statement.

z is proportional to the square root of y.

Short answer

Equation that represents the statement is$\mathrm{z}=\mathrm{k}\sqrt{\mathrm{y}}$.

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

Step 2. Using Direct variation, write an equation where z is proportional with square root of y.

$\mathrm{z}=\mathrm{k}\sqrt{\mathrm{y}}$

Here k is any constant and is not equal to zero.

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

Final equation is:

$\mathrm{z}=\mathrm{k}\sqrt{\mathrm{y}}$