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The equation given is \( 3x + 5y = 30 \). We need to find both the **x-intercept** and the **y-intercept**.

### 1. **X-intercept:**
The x-intercept occurs when \( y = 0 \). Substituting \( y = 0 \) into the equation:

\[
3x + 5(0) = 30 \implies 3x = 30 \implies x = \frac{30}{3} = 10
\]

Thus, the **x-intercept** is \( x = 10 \), which is already provided in the image.

### 2. **Y-intercept:**
The y-intercept occurs when \( x = 0 \). Substituting \( x = 0 \) into the equation:

\[
3(0) + 5y = 30 \implies 5y = 30 \implies y = \frac{30}{5} = 6
\]

Thus, the **y-intercept** is \( y = 6 \).

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Would you like more details on this? Here are some related questions for further exploration:

1. What is the geometric meaning of the x- and y-intercepts?
2. How would you graph the line using the intercepts?
3. Can you rewrite the equation in slope-intercept form?
4. What is the slope of the line in this equation?
5. How would the intercepts change if the constants in the equation were different?

**Tip:** When solving for intercepts, remember that at the x-intercept, \( y = 0 \), and at the y-intercept, \( x = 0 \).

Find the x-intercept and the y-intercept of the graph of the equation: 3x + 5y = 30. The x-intercept is 10. What is the y-intercept?

Solve for the x-intercept and y-intercept of the linear equation 3x + 5y = 30. The x-intercept is 10, and the y-intercept is 6. Learn key algebraic concepts like solving for intercepts in Grades 7-9.

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