The equation \( 2x + 5y = 15 \) represents a linear equation in two variables. There are various ways to approach or analyze this equation, depending on what you want to do with it. Here are a few possibilities:

### 1. **Solving for one variable in terms of the other:**
You can express one variable in terms of the other. For instance, solve for \( y \) in terms of \( x \):
\[
5y = 15 - 2x
\]
\[
y = \frac{15 - 2x}{5}
\]
Or solve for \( x \) in terms of \( y \):
\[
2x = 15 - 5y
\]
\[
x = \frac{15 - 5y}{2}
\]

### 2. **Finding intercepts:**
- **x-intercept:** Set \( y = 0 \), then solve for \( x \):
  \[
  2x = 15 \quad \Rightarrow \quad x = \frac{15}{2}
  \]
  So, the x-intercept is \( \left( \frac{15}{2}, 0 \right) \).

- **y-intercept:** Set \( x = 0 \), then solve for \( y \):
  \[
  5y = 15 \quad \Rightarrow \quad y = 3
  \]
  So, the y-intercept is \( (0, 3) \).

### 3. **Graphing the equation:**
You can plot the equation by finding two points (like the intercepts) and then drawing a line through them.

### 4. **Slope-intercept form:**
The equation can be rewritten in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept:
\[
y = -\frac{2}{5}x + 3
\]
Here, the slope \( m = -\frac{2}{5} \) and the y-intercept is \( 3 \).

### 5. **Standard form:**
This equation is already in standard form \( Ax + By = C \), where \( A = 2 \), \( B = 5 \), and \( C = 15 \).

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Do you want more details on any of these methods, or have any other questions?

Here are 5 related questions:
1. How can we solve this system if we add another equation?
2. How do you determine the slope of a line from its equation?
3. How can we graph this linear equation step by step?
4. Can we find a specific solution for \( x \) and \( y \) given additional constraints?
5. What real-world situations can this equation represent?

**Tip:** In linear equations, the slope tells you how steep the line is, while the intercepts show where the line crosses the axes.

Explore how to solve the linear equation 2x + 5y = 15 by finding intercepts, graphing, and converting to slope-intercept form. This problem covers key algebraic concepts for students in Grades 6-9, including solving for variables and understanding the slope.

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