The equation given is:

\[
x - 8y = -16.
\]

This is also a linear equation in two variables, \(x\) and \(y\). We can solve this equation for either variable in terms of the other.

Let's solve for \(y\) in terms of \(x\):

1. Start with the equation:
   \[
   x - 8y = -16.
   \]

2. Isolate \(y\) by moving \(x\) to the other side:
   \[
   -8y = -x - 16.
   \]

3. Divide every term by \(-8\) to solve for \(y\):
   \[
   y = \frac{-x - 16}{-8}.
   \]

4. Simplify the expression:
   \[
   y = \frac{x}{8} + 2.
   \]

Thus, the equation in slope-intercept form (y = mx + b) is:

\[
y = \frac{1}{8}x + 2.
\]

**Key features of this equation:**

- **Slope (m):** \(\frac{1}{8}\)  
- **Y-intercept (b):** 2

This line has a gentle positive slope, meaning it rises slowly as \(x\) increases. The y-intercept is where the line crosses the y-axis at \(y = 2\).

Would you like more details on graphing this equation or have any specific questions?

Here are some related questions to explore:

1. How do you convert a linear equation into slope-intercept form?
2. What are the steps to find the x-intercept of this line?
3. How does the slope affect the graph of a line?
4. Can we find the coordinates of any points on this line by choosing specific \(x\) values?
5. How do you determine if two lines are parallel or perpendicular?

**Tip:** Always simplify equations step-by-step to make graphing and understanding their properties easier.

Learn how to solve the linear equation x - 8y = -16 step-by-step. This problem covers key algebraic concepts, including linear equations and the slope-intercept form. Suitable for students in Grades 7-9.

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