HELP PLZ !!! Show that the set of points are collinear (a) (-2,-6) (2,-4) and (4,-3) (b) (-5,5) (1,1) and (4,-1) (c) (-5,-6) (-2,0) and (-1,2)

(a) note that as x increases by 4, y increases by 2. Then, as x increases by 2, y increases by 1.

(b) and (c) work the same way. Starting at the first point, note that the changes in y and x have the same ratio.

That is, the slope remains constant, and since the middle point figures in both calculations, all the points lie on the same line.

To determine whether a set of points is collinear, we need to check if the slope between any two points in the set is the same.

(a) (-2,-6), (2,-4), and (4,-3):

Step 1: Determine the slope between each pair of points.
- Slope between (-2,-6) and (2,-4):
slope = (y2 - y1) / (x2 - x1) = (-4 - (-6)) / (2 - (-2)) = 2 / 4 = 1/2
- Slope between (2,-4) and (4,-3):
slope = (y2 - y1) / (x2 - x1) = (-3 - (-4)) / (4 - 2) = 1 / 2 = 1/2

Since the slopes are the same for both pairs of points, we can conclude that the points (-2,-6), (2,-4), and (4,-3) are collinear.

(b) (-5,5), (1,1), and (4,-1):

Step 1: Determine the slope between each pair of points.
- Slope between (-5,5) and (1,1):
slope = (y2 - y1) / (x2 - x1) = (1 - 5) / (1 - (-5)) = -4 / 6 = -2/3
- Slope between (1,1) and (4,-1):
slope = (y2 - y1) / (x2 - x1) = (-1 - 1) / (4 - 1) = -2 / 3 = -2/3

Since the slopes are the same for both pairs of points, we can conclude that the points (-5,5), (1,1), and (4,-1) are collinear.

(c) (-5,-6), (-2,0), and (-1,2):

Step 1: Determine the slope between each pair of points.
- Slope between (-5,-6) and (-2,0):
slope = (y2 - y1) / (x2 - x1) = (0 - (-6)) / (-2 - (-5)) = 6 / 3 = 2
- Slope between (-2,0) and (-1,2):
slope = (y2 - y1) / (x2 - x1) = (2 - 0) / (-1 - (-2)) = 2 / 1 = 2

Since the slopes are the same for both pairs of points, we can conclude that the points (-5,-6), (-2,0), and (-1,2) are collinear.

In summary, the sets of points (a) (-2,-6), (2,-4), and (4,-3), (b) (-5,5), (1,1), and (4,-1), and (c) (-5,-6), (-2,0), and (-1,2) are all collinear.