Final answer:
The equation of a line parallel to 2x + y = 6 that passes through (4, -4) is y = -2x + 4.
Step-by-step explanation:
The equation of a line that is parallel to another line will have the same slope. For the line 2x + y = 6, we first rewrite this in slope-intercept form: y = -2x + 6. Therefore, the slope (m) of this line is -2. A line that passes through the point (4, -4) and is parallel to the given line will also have a slope of -2.
To find the equation of this new line, we use the point-slope form of the line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line (in this case, (4, -4)) and m is the slope. Substituting these values in, we get y - (-4) = -2(x - 4). This simplifies to y + 4 = -2x + 8.
Finally, we write the equation in slope-intercept form, y = mx + b, by isolating y. Our equation becomes y = -2x + 4. Thus, y = -2x + 4 is the equation of the line that passes through the point (4, -4) and is parallel to the line 2x + y = 6.