Final answer:
The given set of points form a line that is neither parallel nor perpendicular.
Step-by-step explanation:
The given set of points (-4,9), (1,-1), (-8,-10), (2,-6) can form a straight line.
To determine if the points are parallel, perpendicular, or neither, we need to calculate the slope of the line passing through each pair of points.
For the points (-4,9) and (1,-1), the slope is calculated as (change in y)/(change in x) = (-1-9)/(1-(-4))
= -10/5
= -2.
For the points (-4,9) and (-8,-10), the slope is calculated as (change in y)/(change in x) = (-10-9)/(-8-(-4))
= -19/-4
= 19/4.
For the points (-4,9) and (2,-6), the slope is calculated as (change in y)/(change in x) = (-6-9)/(2-(-4))
= -15/6
= -5/2.
Since the slopes are not equal for any pair of points, the line passing through these points is neither parallel nor perpendicular to the x-axis.