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To find the slope of the line represented by the equation \( 15x + 3y = 45 \), we first need to rearrange the equation into slope-intercept form, \( y = mx + b \), where \( m \) is the slope.

### Steps:
1. Start with the given equation:
   \[
   15x + 3y = 45
   \]

2. Solve for \( y \):
   \[
   3y = -15x + 45
   \]

3. Divide the entire equation by 3 to isolate \( y \):
   \[
   y = -5x + 15
   \]

Now, the equation is in slope-intercept form \( y = -5x + 15 \). From this, we can see that the slope \( m \) is **-5**.

### Answer:
The slope of the line is \( \boxed{-5} \).

Do you have any further questions or would you like more details on this? Here are some related questions:

1. What does the slope of a line represent in geometry?
2. How do you find the y-intercept of a line in slope-intercept form?
3. How do you convert a line equation from general form to slope-intercept form?
4. Can you find the slope of a vertical line? What is it?
5. How would you calculate the slope if given two points on a line?

**Tip:** In any linear equation, the coefficient of \( x \) in the slope-intercept form always represents the slope.

What is the slope of the line represented by 15x + 3y = 45?

Learn how to find the slope of the line from the equation 15x + 3y = 45 by rearranging it into slope-intercept form. Understand the step-by-step process of isolating y and identifying the slope. Suitable for students in Grades 8-10.

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