To simplify the given equation:

\[ y = \frac{5}{9}x + \frac{5}{18} + \frac{3}{2} \]

We'll follow these steps:

### 1. Find a common denominator for the constants:
The terms \(\frac{5}{18}\) and \(\frac{3}{2}\) need to be combined. The least common denominator between 18 and 2 is 18.

\[
\frac{3}{2} = \frac{3 \times 9}{2 \times 9} = \frac{27}{18}
\]

Now we can add \(\frac{5}{18} + \frac{27}{18}\):

\[
\frac{5}{18} + \frac{27}{18} = \frac{5 + 27}{18} = \frac{32}{18}
\]

This simplifies to:

\[
\frac{32}{18} = \frac{16}{9}
\]

### 2. Rewrite the equation:
Now, the equation becomes:

\[
y = \frac{5}{9}x + \frac{16}{9}
\]

### 3. Factor out the common denominator:
We can factor \(\frac{1}{9}\) from both terms:

\[
y = \frac{1}{9}(5x + 16)
\]

This is the simplified form of the equation.

Would you like more details or clarification on any of these steps?

Here are 5 related questions for practice:
1. How do you simplify fractions with different denominators?
2. What is the process for factoring out common terms from an expression?
3. How do you handle equations involving multiple fractions?
4. How do you convert improper fractions into mixed numbers?
5. What are the steps for finding the least common denominator between two numbers?

**Tip:** When adding fractions, always find the least common denominator to simplify the process.

Learn how to simplify the linear equation y = (5/9)x + 5/18 + 3/2 by combining fractions and factoring out common terms. This step-by-step guide covers important algebraic concepts like finding a common denominator and simplifying fractions. Suitable for Grades 7-9.

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