An algebraic slope is essentially a representation of how steep a line is. A rate of how much a line rises, measured by the y axis, and how far it spans the, measured by the x axis, renders the slope. The symbol for the slope is a lowercase m. It is fairly simple to calculate the slope of a line:
*pick 2 points on the line and write the coordinates of how far it is relative to the horizontal axis and how tall the point lies relative to the vertical y axis (x, y). So, with 2 points identified by x and y it is possible now to figure out the m slope:
*simply subtract one y from the other then one x from the other x
*now place the difference between the y’s over the difference between the x’s
This fraction is the slope, and, as the fraction implies, you can divide to get a numeric value for m.
A simple example may help demonstrate the process of calculating the slope of a line. Let us assume two points:
(x,y) and (x, y)
(6,9) and (9,18)
Subtract the second y from the first: 18- 9 = 9
Then subtract the second x from the first: 9-6 = 3
The slope is m = 9/3 or m = 3 which means for every rise of 3 spaces using the y axis for a reference it will span only 1 space referencing the x axis. With the slope known, one can draw the rest of the line but following from the two points known and connecting additional points based on the slope. So one point started at 6 relative to the x axis and will span by one space so that the next point has a x coordinate of 7. The first point also had a y coordinate of 9, and with a rise of 3, the next y coordinate is 12. This new point is (7, 12).
- A horizontal line has a slope of ZERO meaning it does not change its position to the y axis, but rather spans space by space parallel to the x axis.
I vertical line has an UNDEFINED slope (because it is not possible to divide by zero). But it essentially does the same thing as a horizontal line, it goes space by space but vertically, parallel to the y axis.
Another handy tip the slope m value provides is being able to draw lines parallel—starting at a different point and using the same slope, one can derive a parallel line. Similarly, if the slope of one line is known and another is parallel to that line, the slope can be inferred as equal.
This brief introduction to what an algebraic slope was given with the intention of showing how there is a method to what appears to be madness in math—ultimately all math is a tool for use.