5x+3y=15 find the x-intercept and y-intercept of the graph of each equation

To find the x-intercept and y-intercept of the equation \( 5x + 3y = 15 \), we follow these steps:

### 1. **Finding the x-intercept:**
The x-intercept occurs when \( y = 0 \). To find the x-intercept, substitute \( y = 0 \) into the equation:

\[
5x + 3(0) = 15
\]
\[
5x = 15
\]
\[
x = \frac{15}{5} = 3
\]

So, the x-intercept is \( (3, 0) \).

### 2. **Finding the y-intercept:**
The y-intercept occurs when \( x = 0 \). To find the y-intercept, substitute \( x = 0 \) into the equation:

\[
5(0) + 3y = 15
\]
\[
3y = 15
\]
\[
y = \frac{15}{3} = 5
\]

So, the y-intercept is \( (0, 5) \).

### Summary:
- **x-intercept**: \( (3, 0) \)
- **y-intercept**: \( (0, 5) \)

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you graph a line using intercepts?
2. What does the slope of the line represent in this equation?
3. How do you rewrite the equation \( 5x + 3y = 15 \) in slope-intercept form?
4. How would you find the intercepts of a vertical or horizontal line?
5. How can you check if a point is on the line represented by \( 5x + 3y = 15 \)?

**Tip:** Always substitute one variable as zero to easily find the intercepts of any linear equation.

5x + 3y = 15 find the x-intercept and y-intercept of the graph of each equation

Learn how to find the x-intercept and y-intercept of the linear equation 5x + 3y = 15 with a clear, step-by-step solution. This problem covers key concepts in linear equations and coordinate geometry, suitable for students in Grades 6-8.

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