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To find the **x-intercept** and **y-intercept** of the line given by the equation:

\[
6x - 7y = 42
\]

We can approach the solution as follows:

### 1. Find the **y-intercept**:
The y-intercept occurs where \( x = 0 \). Substitute \( x = 0 \) into the equation:

\[
6(0) - 7y = 42
\]
\[
-7y = 42
\]
\[
y = -6
\]

So, the **y-intercept** is \( (0, -6) \).

### 2. Find the **x-intercept**:
The x-intercept occurs where \( y = 0 \). Substitute \( y = 0 \) into the equation:

\[
6x - 7(0) = 42
\]
\[
6x = 42
\]
\[
x = 7
\]

So, the **x-intercept** is \( (7, 0) \).

### Final Answer:
- **y-intercept**: \( y = -6 \)
- **x-intercept**: \( x = 7 \)

Let me know if you want more details or have any questions!

Here are 5 related questions for further practice:
1. How do you find the slope of a line given its equation in standard form?
2. Can you express this line in slope-intercept form?
3. What is the equation of a line parallel to this one but passing through a different point?
4. How do you find the x- and y-intercepts for a quadratic equation?
5. How would the intercepts change if the equation were \( 6x - 7y = -42 \)?

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

Find the y-intercept and x-intercept of the line 6x - 7y = 42.

Learn how to find the x- and y-intercepts of the linear equation 6x - 7y = 42 using basic algebraic methods. Suitable for students in Grades 8-10.

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