Find the x and y intercepts of the graph of the equation
6x + y = −13. Write your answers as ordered pairs.

To find the \(x\)- and \(y\)-intercepts of the equation \(6x + y = -13\), we need to do the following:

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

\[
6(0) + y = -13
\]
\[
y = -13
\]

So, the \(y\)-intercept is \((0, -13)\).

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

\[
6x + 0 = -13
\]
\[
6x = -13
\]
\[
x = -\frac{13}{6}
\]

So, the \(x\)-intercept is \(\left(-\frac{13}{6}, 0\right)\).

### Final Answer:
- \(x\)-intercept: \(\left(-\frac{13}{6}, 0\right)\)
- \(y\)-intercept: \((0, -13)\)

Would you like more details or have any questions about the steps?

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Here are 5 related questions to expand your understanding:
1. How do you find intercepts for quadratic equations?
2. What does the slope of this equation tell you about the graph?
3. How can you convert this equation into slope-intercept form?
4. How do the intercepts help in graphing a linear equation?
5. What happens to the intercepts if the equation is multiplied by a constant?

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

Find the x and y intercepts of the graph of the equation 6x + y = −13. Write your answers as ordered pairs.

Discover how to find the x and y intercepts of the linear equation 6x + y = -13 with step-by-step solutions. This problem explores key algebra concepts, such as solving for intercepts and working with linear equations. Ideal for students in Grades 8-10.

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