Well this is my thought depending on where the point of dilation is the coordinates of the give plane is determined. The point of dilation not only is main factor that positions the coordinates, but the scale factor has a huge impact on the placement of the coordinates.
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The coordinates of all points in the coordinate plane consist of ordered pairs of numbers.
Two coordinates define a point. You need two pairs of two coordinates to define two points and, therefore, a slope.
No.
It is simply the difference between their y coordinates.
You need two coordinates, not one, to specify a point. To calculate the slope, simply calculate (difference in y-coordinates) / (difference in x-coordinates).