Rise/Run (The rise of the slope divided by the run of the slope.)
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The change in the Y coordinate over the change in the X coordinate of any two points on a line.
if you define y = constant then the slope of any constant is 0 so if you define the line y = 0 the slope of 0 is 0.
If you have any expression that defines a line, you can find the slope of the line. After you have found the slope of the line, you can then write an expression describing the line in slope intercept form. You can't define a slope-intercept form for any nonlinear equation, because the slope is always* changing; there are often several intercepts as well.
Linear functions can be represented by a straight line in space. One way to define a straight line uniquely is to use its slope (or direction vector) and any one point on the line.
The line perpendicular to a line with a slope of 1/5 has a slope of -5.
The slope of a line is undefined if the line is vertical.