https://file.aiquickdraw.com/mathbot/file/1725575865357clxyzqfj.jpg

We are given the equation of a line:

\[
7x + 6y = -11
\]

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

\[
7x + 6(0) = -11
\]
\[
7x = -11
\]
\[
x = \frac{-11}{7}
\]

Thus, the x-intercept is \( x = \frac{-11}{7} \).

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

\[
7(0) + 6y = -11
\]
\[
6y = -11
\]
\[
y = \frac{-11}{6}
\]

Thus, the y-intercept is \( y = \frac{-11}{6} \).

### Summary:
- **x-intercept**: \( \left(\frac{-11}{7}, 0 \right) \)
- **y-intercept**: \( \left(0, \frac{-11}{6} \right) \)

Would you like more details or explanations? Here are 5 related questions:

1. How do you calculate the slope of a line given two intercepts?
2. Can we rewrite the equation \(7x + 6y = -11\) in slope-intercept form?
3. What do intercepts tell us about the graph of the line?
4. How can we find the distance between the x- and y-intercepts?
5. Can you find the intercepts for other types of equations (e.g., quadratic)?

**Tip**: Always remember that the x-intercept and y-intercept provide the points where the line crosses the respective axes, helping to graph the equation easily.

Find the y-intercept and x-intercept of the line 7x + 6y = -11.

Learn how to find the x-intercept and y-intercept of the linear equation 7x + 6y = -11. Step-by-step explanation for solving algebraic linear equations by setting variables to zero.

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