To solve the equation \(3y + 6x = 15\), we can manipulate it to find the values of \(y\) and \(x\). There are several ways to approach this, such as solving for one variable in terms of the other, or finding the intercepts if we are considering it as a linear equation. I'll walk you through solving for \(y\) in terms of \(x\).

### Step 1: Solve for \(y\)
Given:
\[
3y + 6x = 15
\]

Subtract \(6x\) from both sides:
\[
3y = 15 - 6x
\]

Now, divide both sides by 3:
\[
y = \frac{15 - 6x}{3}
\]

Simplify the expression:
\[
y = 5 - 2x
\]

### Interpretation:
The equation can be expressed as \(y = 5 - 2x\), which is the slope-intercept form of the equation, where the slope is \(-2\) and the y-intercept is \(5\).

### Step 2: Solving for Intercepts
- **Y-intercept:** Set \(x = 0\):
  \[
  y = 5 - 2(0) = 5
  \]
  So the y-intercept is \( (0, 5) \).

- **X-intercept:** Set \(y = 0\):
  \[
  0 = 5 - 2x
  \]
  Solving for \(x\):
  \[
  2x = 5 \quad \Rightarrow \quad x = \frac{5}{2}
  \]
  So the x-intercept is \( \left(\frac{5}{2}, 0\right) \).

Would you like more details or have any questions?

### Related Questions:
1. What is the slope of the line represented by the equation \(3y + 6x = 15\)?
2. How would the graph of \(y = 5 - 2x\) look on a coordinate plane?
3. If \(x = 3\), what is the value of \(y\) in the equation \(y = 5 - 2x\)?
4. How would you write the equation \(3y + 6x = 15\) in standard form?
5. Can you express \(x\) in terms of \(y\) from the equation \(3y + 6x = 15\)?

### Tip:
When dealing with linear equations, expressing the equation in slope-intercept form \(y = mx + b\) can help quickly identify the slope and y-intercept for graphing purposes.

Learn how to solve the equation 3y + 6x = 15 step-by-step with detailed explanations. Discover the slope-intercept form and find intercepts. Suitable for students in Grades 7-9 studying linear equations and algebraic concepts.

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