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

\[
13x + 13y = -14
\]

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

\[
13x + 13(0) = -14
\]
\[
13x = -14
\]
\[
x = -\frac{14}{13}
\]

So, the x-intercept is:
\[
\left( -\frac{14}{13}, 0 \right)
\]

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

\[
13(0) + 13y = -14
\]
\[
13y = -14
\]
\[
y = -\frac{14}{13}
\]

So, the y-intercept is:
\[
\left( 0, -\frac{14}{13} \right)
\]

### Final Answer
- **x-intercept**: \(\left( -\frac{14}{13}, 0 \right)\)
- **y-intercept**: \(\left( 0, -\frac{14}{13} \right)\)

Would you like further details on any part of the solution, or have additional questions?

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Here are five questions to deepen understanding:

1. How can you find the intercepts of a line if it’s written in slope-intercept form?
2. What happens to the intercepts if we multiply or divide the entire equation by a constant?
3. Can you verify intercepts graphically to see where the line crosses the axes?
4. How would you solve for intercepts if the equation had different coefficients?
5. What if the equation was in the form \(Ax + By = C\); would the process change?

**Tip:** To quickly find intercepts, set the opposite variable to zero and solve for the remaining one.

Find the x-intercept and y-intercept of the line: 13x + 13y = -14

Learn how to find the x- and y-intercepts of the line 13x + 13y = -14 with a detailed step-by-step solution. This problem covers key algebraic concepts, including solving for intercepts of linear equations. Suitable for students in Grades 9-11.

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