What is the slope of the line between (3,5) and (1, 3 )?

1 Answer
George C.
Nov 23, 2015

#1#

Explanation:

If a line passes through two points #(x_1, y_1)# and #(x_2, y_2)# then its slope #m# is given by the formula:

#m = (Delta y)/(Delta x) = (y_2-y_1)/(x_2-x_1)#

In our example, I would normally pick the points in the reverse order to the one you have specified in order to be working with positive numbers, like so:

#(x_1, y_1) = (1, 3)#

#(x_2, y_2) = (3, 5)#

#m = (y_2-y_1)/(x_2-x_1) = (5-3)/(3-1) = 2/2 = 1#

To demonstrate the the order of the points makes no difference to the result, let's see that with the points the other way round:

#(x_1, y_1) = (3, 5)#

#(x_2, y_2) = (1, 3)#

#m = (y_2-y_1)/(x_2-x_1) = (3-5)/(1-3) = (-2)/(-2) = 1#

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