What is the slope of the line passing through the following points: # (-5, 4) ,(7, -2) #?

1 Answer
Sally
Mar 14, 2016

Slope= #-1/2#

Explanation:

Slope is defined as #(Delta y)/ (Delta x)# . In other words, it is the change in #y# over the change in #x#. When we have two points, we can calculate the slope by subtracting the corresponding values and making them into a ratio.

#x-y# coordinate points are in the form #(x,y)#
We have #(-5,4)# and #(7,-2)#
Let's call #(-5,4)=(x_1,y_1)# and #(7,-2)=(x_2,y_2)#
Now, it doesn't matter which point you choose to subtract from which point- it will work either way, as you can see below when calculating the slope:

#(Delta y)/ (Delta x)=(y_2-y_1)/(x_2-x_1)=(-2-4)/(7--5)=(-2-4)/(7+5)=(-6)/12=-1/2#

Is equivalent to the other way around:

#(Delta y)/ (Delta x)=(y_1-y_2)/(x_1-x_2)=(4--2)/(-5-7)=(4+2)/(-5-7)6/-12=-1/2#

Just make sure you are consistent in the order you subtract.

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