Final answer:
The equation y = -2x - 3 represents a line that is parallel to the line passing through the points (-6,9) and (7,-17).
Step-by-step explanation:
The equation of a line parallel to a given line will have the same slope as the given line. In this case, the line passing through the points (-6,9) and (7,-17) has a slope of -26/13.
So, any equation with a slope of -26/13 will be parallel to this line.
Let's use point-slope form to find the equation of the line.
We'll use the point (-6,9) as a reference point.
The equation will look like y - 9 = (-26/13)(x - (-6)).
Simplifying, we get y - 9 = -2(x + 6), which can be rewritten as y = -2x - 3.
Therefore, the equation y = -2x - 3 represents a line that is parallel to the line passing through the points (-6,9) and (7,-17).