How do you find the slope of (a line passing through the points) (3, -2) and (-2, 5)?

1 Answer
David G.
Feb 1, 2016

You can use the gradient (slope) formula: #m=(y_2-y_1)/(x_2-x_1)#. In this case the slope is #-7/5#.

Explanation:

The slope of a line is often called '#m#', and is defined as #(rise)/(run)#: the amount a line 'rises' vertically (in the #y# direction) for each unit it 'runs' horizontally (in the #x# direction).

A line with a slope of 2 rises by 2 units for every unit it moves onward in #x#, while a line with a slope of #-3# falls by 3 units in #y# for each unit in #x#.

A formula for this is as follows:

#m=(rise)/(run) = (y_2-y_1)/(x_2-x_1)#

We usually use the second point given to us in the question as #(x_2,y_2)# and the first as #(x_1,y_1)# but it doesn't matter : try the experiment for yourself of doing it the other way around, and see that you get the same answer for the slope.

In this case:

#m = (y_2-y_1)/(x_2-x_1) = (5-(-2))/(-2-3) = 7/(-5) = -7/5#

The slope of this line is #-7/5#.

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