It is straightforward to find the slope of a line, if the coordinates of two points are given. We can just plug the coordinates in the formula and calculate it.

Let us find the slope of a line passing through (2, 3) and (-5, 4).Thus, the slope of the line m =

$\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ =

$\frac{4 - 3}{-5 - 2}$ = -

$\frac{1}{7}$If the equation of a line is given, we can identify the slope by writing the equation in slope intercept form, that is in the form y = mx + b.

Suppose the equation of a line is given as 2x + y = 5.

Rewriting the equation in slope intercept form, we get y = -2x + 5, where m = - 2.

Hence, the slope of the line = - 2.

When the graph of a line is given and we need to read the coordinates of two points, then we can determine the slope using the slope formula.

Let us find the slope of line whose graph is given below:

Two points on the line are identified as (2, 3) and (0, -4).

Using the slope formula, m =

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

=

$\frac{-4-3}{0-2}$ =

$\frac{-7}{-2}$ = 3.5