We are tasked with finding the equation of a line that passes through the point $(4, -4)$ and is parallel to the line $2x + y = 6$.

Step 1: Find the slope of the given line

The equation of the line $2x + y = 6$ can be written in slope-intercept form $y = mx + b$, where $m$ is the slope.

$2x + y = 6$ Solve for $y$: $y = -2x + 6$

So, the slope of the given line is $m = -2$.

Step 2: Use the slope-point form

Since parallel lines have the same slope, the slope of the line we need is also $m = -2$. Now, use the point-slope form of a line equation, which is:

$y - y_1 = m(x - x_1)$

Here, $(x_1, y_1) = (4, -4)$ and $m = -2$, so:

$y - (-4) = -2(x - 4)$ Simplifying: $y + 4 = -2(x - 4)$ $y + 4 = -2x + 8$ Now subtract 4 from both sides: $y = -2x + 4$

Final Equation:

The equation of the line is: $y = -2x + 4$

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:

1. How would the equation change if the line passed through a different point?
2. What would the equation be if the line was perpendicular instead of parallel?
3. Can you write the equation of the line in standard form?
4. How can you verify that two lines are parallel using their equations?
5. How would the problem change if the given equation was in a different form?

Tip: To quickly find the slope of a line from an equation, always convert the equation to the slope-intercept form $y = mx + b$, where $m$ is the slope.