. If
𝑥
x varies directly as
𝑦
y and
𝑥
=
35
x=35 and
𝑦
=
7
y=7, what is the value of
𝑦
y when
𝑥
=
25?

Since \( x \) varies directly as \( y \), we can express this relationship as:

\[
x = k \cdot y
\]

where \( k \) is the constant of proportionality.

### Step 1: Find the constant \( k \)

Given that \( x = 35 \) when \( y = 7 \), we can substitute these values into the equation:

\[
35 = k \cdot 7
\]

Solving for \( k \):

\[
k = \frac{35}{7} = 5
\]

### Step 2: Use the constant \( k \) to find \( y \) when \( x = 25 \)

Now, we can use the equation \( x = 5 \cdot y \) and substitute \( x = 25 \):

\[
25 = 5 \cdot y
\]

Solving for \( y \):

\[
y = \frac{25}{5} = 5
\]

Thus, the value of \( y \) when \( x = 25 \) is \( y = 5 \).

---

Would you like further details or clarifications on any step?

### Related Questions:
1. How would you solve if \( x \) varies inversely with \( y \)?
2. What happens if both \( x \) and \( y \) vary directly with another variable?
3. How would the equation change if \( x \) varied as the square of \( y \)?
4. Can you find \( y \) if \( x = 50 \) under the same direct variation rule?
5. What if \( y = 10 \) and you needed to find \( x \)?

### Tip:
For direct variation problems, remember that the ratio \( \frac{x}{y} \) remains constant.

If x varies directly as y and x = 35 and y = 7, what is the value of y when x = 25?

Learn how to solve a direct variation problem where x varies directly with y. Given x = 35 and y = 7, find the value of y when x = 25 using the proportionality constant. Suitable for Grades 6-8.

Math Problem Statement

. If 𝑥 x varies directly as 𝑦 y and 𝑥

35 x=35 and 𝑦

7 y=7, what is the value of 𝑦 y when 𝑥

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