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To find the x-intercept and y-intercept of the given line, we need to follow these steps. The equation provided is:

\[
7x - 6y = 42
\]

### 1. Finding the **x-intercept**:
The x-intercept is the point where the line crosses the x-axis. At this point, \( y = 0 \).

Substitute \( y = 0 \) into the equation:

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

Simplify:

\[
7x = 42
\]

Now, solve for \( x \):

\[
x = \frac{42}{7} = 6
\]

Thus, the **x-intercept** is \( (6, 0) \).

### 2. Finding the **y-intercept**:
The y-intercept is the point where the line crosses the y-axis. At this point, \( x = 0 \).

Substitute \( x = 0 \) into the equation:

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

Simplify:

\[
-6y = 42
\]

Now, solve for \( y \):

\[
y = \frac{42}{-6} = -7
\]

Thus, the **y-intercept** is \( (0, -7) \).

### Conclusion:
- **x-intercept**: \( (6, 0) \)
- **y-intercept**: \( (0, -7) \)

Would you like a more detailed explanation of any part of the solution?

Here are some related questions for further exploration:
1. How do we find the slope of the given line from the equation?
2. Can we rewrite the equation in slope-intercept form?
3. How do x- and y-intercepts help in graphing a line?
4. What would change if the equation were multiplied by a constant?
5. Can we use another method to verify the intercepts?

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

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

Learn how to find the x-intercept and y-intercept for the linear equation 7x - 6y = 42. This tutorial provides step-by-step calculations and covers important concepts in linear equations and coordinate geometry. Ideal for students in Grades 8-10.

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