SOLUTION: Determine the slope of the line that passes through the points (-6, -4) and (7, -5)

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Question 1128412: Determine the slope of the line that passes through the points (-6, -4) and (7, -5)
Found 3 solutions by Edwin McCravy, greenestamps, ikleyn:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
We plot the two points and draw the line:



We draw a horizontal green line from the left point until it is
exactly above the right point, like this:



We count the number of units which is the length of the green line.
We count 13.  That number is called the RUN.

We draw a red vertical line from the right end of the green line
down to the line that we want to find the slope of, like this:



We count the number of units which is the length of the red line.
We count only 1 unit.  But since it goes DOWN from the green line to the
given line, we make it NEGATIVE.  So it is -1. That number -1 is called 
the RISE.

The definition of slope is 

Edwin
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


One way to find the slope is to blindly plug numbers into the magical slope formula,



I recommend NOT finding the slope that way. It's too easy to get the wrong numbers in the wrong places and end up with the wrong slope -- especially if you aren't sure of the meaning of the x1, y1, x2, and y2.

You will have a much better understanding of the whole concept of slope if you get the answer by drawing a quick rough sketch of the two points and the line containing them.

Slope is a measure of how much you go up or down compared to how far you go forward, when "walking" along the line from left to right.

In this problem it is 13 "steps" from -6 to +7; in taking those 13 steps forward, you go down 1, from -4 to -5. So you went down 1 step in taking 13 steps forward; the slope is -1/13.
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.

In opposite to tutor @greenestamps, I recommend you ALWAYS use the formula


    m =  =  =  = 


to calculate the slope and do not afraid to substitute negative numbers and calculate fractions.


The only case when it doesn't work is when x1 = x2.

Then the line is VERTICAL and the slope is not defined.

---------------

It is how each and every educated student must do it.


See the lesson
    - Find the slope of a straight line in a coordinate plane passing through two given points
in this site.



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