To find the intercepts of the equation \(-x - 6y = 30\), we need to find both the **x-intercept** (where \(y = 0\)) and the **y-intercept** (where \(x = 0\)).

### 1. Finding the **x-intercept**:
At the x-intercept, \(y = 0\). Substitute \(y = 0\) into the equation:
\[
-x - 6(0) = 30
\]
\[
-x = 30
\]
\[
x = -30
\]
Thus, the **x-intercept** is at \((-30, 0)\).

### 2. Finding the **y-intercept**:
At the y-intercept, \(x = 0\). Substitute \(x = 0\) into the equation:
\[
-(0) - 6y = 30
\]
\[
-6y = 30
\]
\[
y = -5
\]
Thus, the **y-intercept** is at \((0, -5)\).

### Final Answer:
- **x-intercept**: \((-30, 0)\)
- **y-intercept**: \((0, -5)\)

Would you like any further clarification or details on this? 

Here are some related questions:
1. How can intercepts help in graphing a linear equation?
2. What is the slope of this line, and how can we find it?
3. How do x- and y-intercepts relate to the general form of a line equation?
4. How would you find intercepts for a nonlinear equation?
5. Can we rewrite the equation in slope-intercept form?

**Tip**: Intercepts are useful points for quickly sketching a graph without needing to calculate many values!

Learn how to find the x and y intercepts of the linear equation -x - 6y = 30. This step-by-step solution explains key algebraic concepts, including intercepts and solving for variables. Suitable for students in Grades 8-10.

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