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It is the derivative of the vertical change relative to the horizontal change - if the derivative exists. So, with the typical x-y graph, it would be dy/dx. If the graph is a straight line, then it is the change in the vertical positions between any two points divided by the change in the horizontal positions between the same two points (in the same order).
yes because horizontal lines are across and vertical lines is up n down
Yes.
On the horizontal axis you would probably plot the time. On the vertical axis you could plot displacement, velocity or acceleration.
A vertical line has an undefined slope. If a line is vertical, the horizontal coordinate, commonly known as the x coordinates, must all be the same. If not, the line would not be vertical.