To find the equation of the line that contains the points (-6, 2) and (9, -8), we need to use the point-slope formula:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is any point on the line.
First, we need to find the slope of the line:
m = (y2 - y1)/(x2 - x1)
= (-8 - 2)/(9 + 6)
= -10/15
= -2/3
Now, we can use one of the given points, let's say (-6, 2), and plug in the values we just found into the point-slope formula:
y - 2 = (-2/3)(x - (-6))
y - 2 = (-2/3)(x + 6)
y - 2 = (-2/3)x - 4
y = (-2/3)x - 2
Therefore, the equation of the line that contains the points (-6, 2) and (9, -8) is y = (-2/3)x - 2, which is not represented by any of the given options.