Final answer:
The equations y = -x - 6 and 2x + 2y = 12 (which rearranges to y = -x + 6) are parallel to the line y = -x + 12 because they share the same slope of -1.
Step-by-step explanation:
To identify the equation of a line that is parallel to the graph of the line y = -x + 12, we need to look for lines that have the same slope. The slope of this reference line is -1 (the coefficient of x). Let's evaluate each option:
- y = -x - 6: This equation has a slope of -1, which is the same as the slope of the reference line, so it is parallel.
- 2x + 2y = 12: If we rearrange this equation into slope-intercept form (y = mx + b), we get y = -x + 6. This equation also has a slope of -1 and is thus parallel.
- 2x - 2y = 12: Again, rearranging into slope-intercept form gives us y = x - 6. The slope here is +1, which is not the same as the reference line, so it's not parallel.
- y = x - 6: This equation clearly has a slope of +1, so it's not parallel to the reference line.
Only the equations y = -x - 6 and when rearranged, 2x + 2y = 12 (which becomes y = -x + 6), are parallel to the reference line y = -x + 12.