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The equation provided is \( 6x + 2y = -4 \). 

We need to determine if this defines \( y \) as a linear function of \( x \) and, if so, express it in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Let's solve the equation for \( y \):

1. Start with the equation:
   \[
   6x + 2y = -4
   \]

2. Subtract \( 6x \) from both sides:
   \[
   2y = -6x - 4
   \]

3. Divide everything by 2 to isolate \( y \):
   \[
   y = -3x - 2
   \]

This is in the form \( y = mx + b \), where \( m = -3 \) and \( b = -2 \). Therefore, the equation defines \( y \) as a linear function of \( x \), and the function is:

\[
y = -3x - 2
\]

### Do you need more details or have any questions?

Here are 5 related questions to expand on this concept:

1. What is the slope of a line, and how does it affect the graph of the linear equation?
2. How can you find the x-intercept and y-intercept of a linear equation?
3. How do you determine if two lines are parallel or perpendicular based on their equations?
4. What are other common forms of linear equations besides the slope-intercept form?
5. Can linear equations have any other degrees besides 1?

**Tip:** To graph a linear equation, always start by plotting the y-intercept and then use the slope to determine the direction and steepness of the line.

Determine whether the equation defines y as a linear function of x: 6x + 2y = -4

Learn how to solve the linear equation 6x + 2y = -4, express it in slope-intercept form y = mx + b, and understand the key concepts involved. Suitable for students in Grades 8-10.

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