If y varies directly with x and y=72 when x=
–
8, find x when y=
–
27

If \( y \) varies directly with \( x \), it means the relationship between them can be expressed as:

\[
y = kx
\]

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

### Step 1: Find the Constant of Proportionality
We are given that \( y = 72 \) when \( x = -8 \). Plug these values into the equation:

\[
72 = k(-8)
\]

\[
k = \frac{72}{-8}
\]

\[
k = -9
\]

### Step 2: Find \( x \) When \( y = -27 \)
Now that we know \( k = -9 \), we use the equation again:

\[
-27 = -9x
\]

\[
x = \frac{-27}{-9}
\]

\[
x = 3
\]

### Final Answer
The value of \( x \) when \( y = -27 \) is:

\[
\boxed{3}
\]

Would you like a detailed explanation of the steps, or do you have any questions? Here are some related questions:

1. What does it mean when two variables vary directly?
2. How would you find the constant of proportionality if \( y \) and \( x \) are given as fractions?
3. Can you solve a problem where \( y \) varies directly with \( x \) and \( y \) is negative when \( x \) is positive?
4. What happens if \( y \) varies inversely with \( x \)? How would the equation change?
5. If \( y = kx \) and \( k \) is zero, what does that imply about the relationship between \( y \) and \( x \)?

**Tip:** Always isolate the constant of proportionality first; it simplifies solving for other variables later.

If y varies directly with x and y = 72 when x = -8, find x when y = -27

Solve a direct variation problem where y varies directly with x. Given y = 72 when x = -8, learn how to find x when y = -27. This problem covers the concept of direct proportionality and is suitable for students in Grades 7-9.

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