3x+2y=45                                                                   

The equation given is:

\[ 3x + 2y = 45 \]

This is a linear equation in two variables, \(x\) and \(y\). Here are a few ways we can approach this:

### 1. **Solve for \(y\) in terms of \(x\):**
   \[
   2y = 45 - 3x
   \]
   \[
   y = \frac{45 - 3x}{2}
   \]

### 2. **Solve for \(x\) in terms of \(y\):**
   \[
   3x = 45 - 2y
   \]
   \[
   x = \frac{45 - 2y}{3}
   \]

### 3. **Find specific solutions:**
   We can find specific solutions by substituting values for one variable and solving for the other. For example:

   - If \(x = 0\):
     \[
     3(0) + 2y = 45 \implies y = \frac{45}{2} = 22.5
     \]

   - If \(y = 0\):
     \[
     3x + 2(0) = 45 \implies x = \frac{45}{3} = 15
     \]

### 4. **Graphical representation:**
   The equation represents a straight line in the Cartesian plane. The slope of the line is \(-\frac{3}{2}\), and the y-intercept is \(\frac{45}{2}\).

Would you like more details on any of these approaches or have specific questions? 

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Here are 5 related questions you might find interesting:

1. How do you find the intersection point of two linear equations?
2. What is the significance of the slope in a linear equation?
3. How do you determine if a point lies on the line represented by the equation \(3x + 2y = 45\)?
4. What are the steps to graph a linear equation?
5. How do you find the equation of a line parallel or perpendicular to \(3x + 2y = 45\)?

**Tip:** For any linear equation in two variables, you can always express one variable in terms of the other and generate a set of solutions or points that satisfy the equation.

Learn how to solve the linear equation 3x + 2y = 45 with detailed methods including solving for variables, finding specific solutions, and graphical representation. Understand the concepts of linear equations in two variables and their applications. Suitable for students in Grades 7-9.

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