Question 448485
What's the slope of the line that goes through 
these pair of points: (6,8) and (8,9) ?
 <pre><font face = "consolas" color = "indigo" size = 4><b>

Plot the two points:

{{{drawing(400,400,-2,11,-2,11,

graph(400,400,-2,11,-2,11), circle(6,8,.1), circle(8,9,.1),
locate(6,8,"(6,8)"), locate(8,9,"(8,9)") )}}}

Draw a straight line through them:

{{{drawing(400,400,-2,11,-2,11,
line(-6,2,13,11.5),
graph(400,400,-2,11,-2,11), circle(6,8,.1), circle(8,9,.1),
locate(6,8,"(6,8)"), locate(8,9,"(8,9)") )}}}

The line goes uphill to the right, so its slope
will be a positive number.

Draw a green line from (6,8) till it is exactly below (8,9).

{{{drawing(400,400,-2,11,-2,11,
green(line(6,8,8,8),line(6,0,8,0)), line(-6,2,13,11.5),
graph(400,400,-2,11,-2,11), circle(6,8,.1), circle(8,9,.1),
locate(6,8,"(6,8)"), locate(8,9,"(8,9)") )}}}

That green line is called a "run". Notice that it is 2 units
long,  So the run is 2

Next draw a red line from the end of the green line up to the
point (8,9).

{{{drawing(400,400,-2,11,-2,11,
green(line(6,8,8,8)), red(line(8,8,8,9)),
line(-6,2,13,11.5),
graph(400,400,-2,11,-2,11), circle(6,8,.1), circle(8,9,.1),
locate(6,8,"(6,8)"), locate(8,9,"(8,9)") )}}}

That red line is called a "rise". Notice that it is 1 unit
long,  So the rise is 1.

Now the slope is defined as {{{(rise)/(run) = 1/2}}}

So the slope is 1/2, positive because it goes uphill to
the right.  Lines that go downhill to the right have
slopes which are negative.

Edwin</pre>