The constant rate of change between two points on a line is called slope.
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The run (not runs - which means diarrhoea) is the horizontal change between two points.
A line is the locus of points such that the gradient (slope) between that point and one fixed point in the plane is a constant. Technically, that definition does not include a vertical line because its gradient is not defined! You could get around that this by requiring that either the gradient is a constant or, if it is undefined, then the inverse gradient (dx/dy) is constant.
The tangent line is the instantaneous rate of change at a point on a curve. The secant line crosses a curve twice at points A and B, representing the average rate of change between those two points.
A straight line is the shortest distance between two points, a line is the delineation of a connection between two or more points.
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