Question

True or false? The Gradient between adjacent pairs of points are equal,the points are collinear. Thanks

Answer 1

True.
A series of three or more points must be collinear if the gradients between them are equal to one another.

Explanation:

If the gradients between three or more successive pairs of points
are equals, then the string of points must be collinear.

http://math.tutorvista.com/geometry/collinear-points.html

In this image, the slopes between any two of the three points are all equal to one another.

A test for collinear points is to establish that the slopes are equal.
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Here is another way to determine if three points are collinear.

If three points are not collinear, then lines drawn between them will form a triangle.

The greater the distance of the third point from the line formed by the other two points, the greater the area of the triangle.

That means that by logic, if the points are collinear, the area of the triangle is zero.
And if the area of a triangle is zero, then the points are collinear.
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Another way to establish that three or more points are collinear is to show that the distances between all the pairs are equal.
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A trivial instance of collinear points is the line between exactly two points.
Any two points define a line.

You can find out more about this here:
http://www.math-for-all-grades.com/Collinear-points.html