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.