What is the slope of a straight line?

The slope is used to measure the inclination of a straight line regarding the abscissa axis (the `x`-axis). For instance, a straight line with a slope 2, according to an ordinary language, can be explained as it follows: for each two units the straight line vertically “goes up”, it horizontally “goes forward” one unit.

There are several ways to find the value of that slope:

• If we know the equation of the straight line, `y = mx + b`, the slope value will be `m`. For instance, if we have the equation `y = 3x + 1` the slope of this straight line will be `3`.


• If we have been given two points through which the straight line goes through, we can use the following formula: `m=(y_1-y_2)/(x_1-x_2)` . For instance, a straight line that goes through the points `A(4, 7)` and `B(2, 3)` its slope can be calculated by using the following operation: `m=(7-3)/(4-2) hArr m=4/2 hArr m=2` . We can then say it has a slope 2.


• It can also be calculated if we know the smallest positive angle made by the straight line together with the x-axis. To do so it will be enough to use the following formula: `m = tg alpha`. For instance, if the angle is 45º then it will have a slope 1 because `m = tg(45º) hArr m = 1`.


• Finally it can be obtained if we know the director vector of the straight line, through the following relation: `m = u_2/u_1`. For instance, if the vector of a straight line has the following coordinates `vec u = (2,8)` so the slope is calculated through `m = 8/2 hArr m = 4`.

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