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To solve the problem and graph the line represented by the equation \(3x + 5y = 15\), we need to find the x-intercept and y-intercept.

### Finding the Intercepts

1. **X-intercept**:
   - The x-intercept occurs when \(y = 0\).
   - Substitute \(y = 0\) into the equation \(3x + 5y = 15\):
     \[
     3x + 5(0) = 15 \implies 3x = 15 \implies x = 5
     \]
   - The x-intercept is \((5, 0)\).

2. **Y-intercept**:
   - The y-intercept occurs when \(x = 0\).
   - Substitute \(x = 0\) into the equation \(3x + 5y = 15\):
     \[
     3(0) + 5y = 15 \implies 5y = 15 \implies y = 3
     \]
   - The y-intercept is \((0, 3)\).

### Plotting the Points and Graphing the Line

1. Plot the x-intercept \((5, 0)\) on the graph.
2. Plot the y-intercept \((0, 3)\) on the graph.
3. Draw a line through these two points to represent the equation \(3x + 5y = 15\).

Here's a detailed solution:
- The x-intercept is at point \((5, 0)\).
- The y-intercept is at point \((0, 3)\).
- Use these two points to draw the line.

Would you like further details or have any questions about the process? Here are some related questions to consider:

1. How do you find the x-intercept and y-intercept of a different linear equation?
2. What are the steps to convert a linear equation into slope-intercept form?
3. How can you determine if a point lies on the line given by a linear equation?
4. What are the characteristics of parallel and perpendicular lines in terms of their slopes?
5. How do you graph a line given its slope and one point on the line?

**Tip:** Always verify your intercepts by substituting back into the original equation to ensure accuracy.

Use the dot tool to plot the x- and y-intercepts of the equation 3x + 5y = 15, then draw a line through these points.

Learn how to graph the line represented by 3x + 5y = 15 by finding the x-intercept and y-intercept and drawing a line through these points. Ideal for students in Grades 7-10 covering linear equations and graphing concepts.

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