The equation you provided is:

\[
12x - 20y = -100
\]

This is a linear equation in two variables \(x\) and \(y\). We can solve it for one variable in terms of the other, or approach it in various ways depending on your goal. Here are a couple of possible approaches:

### 1. Solving for \(x\):
\[
12x = 20y - 100
\]
\[
x = \frac{20y - 100}{12}
\]
Simplifying further:
\[
x = \frac{5y - 25}{3}
\]

### 2. Solving for \(y\):
\[
-20y = -12x - 100
\]
\[
y = \frac{12x + 100}{20}
\]
Simplifying further:
\[
y = \frac{3x + 25}{5}
\]

Would you like to solve this further, or plug in specific values for \(x\) or \(y\)?

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Here are 5 follow-up questions you could explore:

1. What are the intercepts of the equation \(12x - 20y = -100\)?
2. How do you graph the line represented by this equation?
3. What is the slope of the line in the equation?
4. How would you solve this equation if it were part of a system of equations?
5. How does changing the coefficients affect the slope and intercepts?

**Tip**: When solving linear equations, rearrange terms carefully to keep track of signs and coefficients!

Explore how to solve the linear equation 12x - 20y = -100 with a step-by-step breakdown. This guide covers rearranging terms, finding x and y, and understanding key algebraic concepts such as slope and intercepts. Suitable for students in Grades 8-10.

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