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The equation provided is \( 7x + 9y = 6y - 4 \), and we are asked to express this equation in slope-intercept form. 

### Step-by-step solution:

1. Start with the given equation:
   \[
   7x + 9y = 6y - 4
   \]

2. Move all the terms involving \( y \) to one side:
   \[
   7x + 9y - 6y = -4
   \]
   Simplifying the \( y \)-terms:
   \[
   7x + 3y = -4
   \]

3. Now, isolate \( y \) by subtracting \( 7x \) from both sides:
   \[
   3y = -7x - 4
   \]

4. Finally, divide both sides by 3 to solve for \( y \):
   \[
   y = \frac{-7x - 4}{3}
   \]

5. Simplify:
   \[
   y = -\frac{7}{3}x - \frac{4}{3}
   \]

So, the equation in slope-intercept form is:
\[
y = -\frac{7}{3}x - \frac{4}{3}
\]

Would you like further details or clarification on this? Here are five related questions to deepen your understanding:

1. How do you determine the slope and y-intercept from the slope-intercept form of a linear equation?
2. What is the significance of the slope in a linear equation?
3. How would you graph this equation on a coordinate plane?
4. Can you rewrite the equation in standard form \( Ax + By = C \)?
5. What happens to the graph if the slope or the y-intercept changes?

**Tip**: When converting to slope-intercept form, always ensure \( y \) is isolated on one side for easy identification of the slope and intercept!

Express the equation 7x + 9y = 6y - 4 in slope-intercept form.

Learn how to convert the linear equation 7x + 9y = 6y - 4 into slope-intercept form. This problem focuses on algebraic manipulation and simplification of linear equations. Suitable for students in Grades 8-10.

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