Calculation of slope

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O slope of a line is a value that indicates the slope of the line in relation to the abscissa axis (x axis).

There are a few different ways to calculate the slope, let's see what they are?

Calculation of slope

Consider, for example, the line in the figure below:

The slope corresponds to tangent of the angle $\dpi{120} \alpha$ . Thus, representing the slope by the letter $\dpi{120} m$ , We have to:

$\dpi{120} m = tan\: (\alpha)$

And we can establish some different ways to calculate the slope.

Calculating the slope from the angle

Knowing the angle of inclination, just calculate the tangent of that angle.

Example: if $\dpi{120} \alpha = 45^{\circ}$ , then:

$\dpi{120} m = tan\: (\alpha)$

$\dpi{120} m = tan\: (45^{\circ})$

$\dpi{120} m = 1$

To know the value of the tangent of an angle, just consult a trigonometric table.

Calculation of slope from two points

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If we know two points that belong to the line, $\dpi{120} \mathrm{P(x_1,y_1)}$ and $\dpi{120} \mathrm{P(x_2,y_2)}$ , we can calculate the slope as follows:

$\dpi{120} m = \frac{\mathrm{y_2 - y_1}}{\mathrm{x_2-x_1}}$

To understand this formula, notice that in the figure, a right triangle, with $\dpi{120} sin \, (\alpha) =\mathrm{ y_2 - y_1}$ and $\dpi{120} cos \, (\alpha) =\mathrm{ x_2 - x_1}$ and remember that $\dpi{120} tan(\alpha) = \frac{sen(\alpha)}{cos(\alpha)}$ .