Question 566107
<pre>
There are two methods.  By graph, and by formula.  Plot the two points:

(7,-2) and (-1,-5)

{{{drawing(400,400,-4,10,-8,6, graph(400,400,-4,10,-8,6),
circle(7,-2,.1), circle(-1,-5,.1)  )}}}

Draw a line through them

{{{drawing(400,400,-4,10,-8,6, graph(400,400,-4,10,-8,6),
triangle(-9,-8,-17,-11,15,1),
circle(7,-2,.1), circle(-1,-5,.1)  )}}}

Draw a green run and a red rise:

{{{drawing(400,400,-4,10,-8,6, graph(400,400,-4,10,-8,6),
triangle(-9,-8,-17,-11,15,1),
green(line(-1,-5,7,-5)), red(line(7,-5,7,-2)),

circle(7,-2,.1), circle(-1,-5,.1)  )}}}

Count how many units the green run is long:

{{{drawing(400,400,-4,10,-8,6, graph(400,400,-4,10,-8,6),
triangle(-9,-8,-17,-11,15,1),
green(line(-1,-5,7,-5)), red(line(7,-5,7,-2)),

circle(0,-5,.1), circle(1,-5,.1), circle(2,-5,.1), circle(3,-5,.1), circle(4,-5,.1), circle(5,-5,.1), circle(6,-5,.1),circle(7,-5,.1),

circle(7,-2,.1), circle(-1,-5,.1)  )}}}

So we see that the run is 8 units ling.

Next, count how many units the red rise is long:

{{{drawing(400,400,-4,10,-8,6, graph(400,400,-4,10,-8,6),
triangle(-9,-8,-17,-11,15,1),
green(line(-1,-5,7,-5)), red(line(7,-5,7,-2)),

circle(0,-5,.1), circle(1,-5,.1), circle(2,-5,.1), circle(3,-5,.1), circle(4,-5,.1), circle(5,-5,.1), circle(6,-5,.1),circle(7,-5,.1),

circle(7,-5,.1),circle(7,-4,.1),circle(7,-3,.1),circle(7,-2,.1),


circle(7,-2,.1), circle(-1,-5,.1)  )}}}

So we see that the rise is 3 units long.

To get the slope we put the rise over the run, like this:

slope = {{{(rise)/(run)}}} = {{{3/8}}}

That's the answer.

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

Method 2: by the slope formula
 
m = {{{(y[2]-y[1])/(x[2]-x[1])}}} with (x<sub>1</sub>, y<sub>1</sub>) = (7,-2) and (x<sub>2</sub>, y<sub>2</sub>) = (-1,-5)

m = {{{((-5)-(-2))/((-1)-(7))}}} = {{{(-5+2)/(-1-7)}}} = {{{(-3)/(-8)}}} = {{{3/8}}}

Even if you use the slope formula, you must realize that what you actually
have is a measurement of the steepness of the line that connects the two
points, and not just a number to put on a test so the teacher will mark it
correct. :)

Edwin</pre>