The given equation is:

\[
4x + 3y = 12
\]

This is a linear equation in two variables, \(x\) and \(y\). Here's what we can do with this equation:

### Solve for \(y\) in terms of \(x\):
1. Subtract \(4x\) from both sides:
   \[
   3y = 12 - 4x
   \]
2. Divide both sides by 3 to solve for \(y\):
   \[
   y = \frac{12 - 4x}{3}
   \]
   Simplifying the right-hand side:
   \[
   y = 4 - \frac{4}{3}x
   \]

So, \(y = 4 - \frac{4}{3}x\) is the equation in slope-intercept form (\(y = mx + b\)), where the slope is \(-\frac{4}{3}\) and the y-intercept is 4.

Would you like to solve for \(x\) in terms of \(y\), graph the equation, or ask anything specific about this equation?

Here are 5 related questions you might find useful:
1. How do we find the slope of a line from a linear equation?
2. What is the interpretation of the slope in a linear equation?
3. How can we determine the x- and y-intercepts from this equation?
4. Can we solve this equation using substitution or elimination with another equation?
5. How would we graph this equation step-by-step?

**Tip**: The slope tells you how much the value of \(y\) changes for every unit increase in \(x\).

Explore how to solve the linear equation 4x + 3y = 12, rearranging the equation into slope-intercept form. Learn about the slope and y-intercept, perfect for students in Grades 7-9.

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