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The given equation for the bamboo plant's height is:

\[
y = \frac{15}{5}x + 12
\]

This simplifies to:

\[
y = 3x + 12
\]

where:
- \( y \) is the height of the bamboo in inches,
- \( x \) is the number of months.

We are asked to find after how many months (\(x\)) the bamboo plant will be 66 inches tall. So, set \( y = 66 \) and solve for \(x\):

\[
66 = 3x + 12
\]

### Step-by-step solution:
1. Subtract 12 from both sides:
   \[
   66 - 12 = 3x
   \]
   \[
   54 = 3x
   \]

2. Divide both sides by 3:
   \[
   x = \frac{54}{3}
   \]
   \[
   x = 18
   \]

Thus, the bamboo plant will be 66 inches tall after **18 months**.

Would you like further details or have any questions? Here are some related problems to deepen your understanding:

1. What will be the height of the bamboo plant after 10 months?
2. How many months will it take for the bamboo plant to be 90 inches tall?
3. What is the initial height of the bamboo plant when \(x = 0\)?
4. Can you rewrite the equation of the bamboo growth in slope-intercept form? What does the slope represent?
5. If the growth rate changes to 4 inches per month, how would the equation change?

**Tip:** When solving linear equations, always isolate the variable step-by-step for a clearer understanding of each operation.

After how many months will the bamboo plant be 66 inches tall? Given equation is y = (15/5)x + 12.

Solve a linear equation related to bamboo growth, where the equation y = (15/5)x + 12 models the height of the bamboo plant in inches. Learn how many months it will take for the bamboo to reach 66 inches in height. Suitable for Grades 6-8.

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