```Question 359902
<pre>

Two method, graphical and formula:

Graphical:

{{{drawing(400,400,-1,8,-1,8,

graph(400,400,-1,8,-1,8),

line(2+.1,5,2-.1,5),line(2,5+.1,2,5-.1),line(2+.1,5+.1,2-.1,5-.1),line(2+.1,5-.1,2-.1,5+.1),locate(2,5,"(2,5)"),

line(3+.1,6,3-.1,6),line(3,6+.1,3,6-.1),line(3+.1,6+.1,3-.1,6-.1),line(3+.1,6-.1,3-.1,6+.1),locate(3,6,"(3,6)")

)}}}

draw the line:

{{{drawing(400,400,-1,8,-1,8,

graph(400,400,-1,8,-1,8),

line(2+.1,5,2-.1,5),line(2,5+.1,2,5-.1),line(2+.1,5+.1,2-.1,5-.1),line(2+.1,5-.1,2-.1,5+.1),locate(2,5,"(2,5)"),

line(3+.1,6,3-.1,6),line(3,6+.1,3,6-.1),line(3+.1,6+.1,3-.1,6-.1),line(3+.1,6-.1,3-.1,6+.1),locate(3,6,"(3,6)"), green(line(-7,-4,10,13))

)}}}

Draw a horizontal line with one end at one point and the other end
exactly below or above the other point, then

draw a vertical line from there directly to the other point.

You can do that either of these two ways:

{{{drawing(400,400,-1,8,-1,8,

graph(400,400,-1,8,-1,8),
red(line(2,5,3,5),line(3,5,3,6)),
line(2+.1,5,2-.1,5),line(2,5+.1,2,5-.1),line(2+.1,5+.1,2-.1,5-.1),line(2+.1,5-.1,2-.1,5+.1),locate(2,5,"(2,5)"), green(line(-7,-4,10,13)),

line(3+.1,6,3-.1,6),line(3,6+.1,3,6-.1),line(3+.1,6+.1,3-.1,6-.1),line(3+.1,6-.1,3-.1,6+.1),locate(3,6,"(3,6)")

)}}}   {{{drawing(400,400,-1,8,-1,8,

graph(400,400,-1,8,-1,8),

line(2+.1,5,2-.1,5),line(2,5+.1,2,5-.1),line(2+.1,5+.1,2-.1,5-.1),line(2+.1,5-.1,2-.1,5+.1),locate(2,5,"(2,5)"),

line(3+.1,6,3-.1,6),line(3,6+.1,3,6-.1),line(3+.1,6+.1,3-.1,6-.1),line(3+.1,6-.1,3-.1,6+.1),locate(3,6,"(3,6)"), green(line(-7,-4,10,13)),
red(line(2,5,2,6),line(2,6,3,6))

)}}}

The slope is the length of the red vertical line over the
length of the red horizontal line,  and the slope is positive
if the line rises to the right and negative if it falls to the
right.

For this case the vertical line is 1 unit long and the horizontal
line is 1 unit long, and the line rises to the right, so its slope
is {{{""+1/1}}} or 1.

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

By memorized formula:

{{{m = (y[2]-y[1])/(x[2]-x[1])}}}

{{{m = ((6)-(5))/((3)-(2))}}}

{{{m = 1/1}}}

{{{m = 1}}}

Though the memorized formula is easier, the graphical method
shows what slope is all about -- namely how steep a line is and
whether it rises or falls to the right.  If a line has a slope of
exactly 1, then it goes up at an angle of 45 degrees (such as this
line, which goes up at a 45° angle).  If a line has a slope more
than 1, it goes up steeper than 45 degrees, and if its slope is less
than 1, it goes up less steep than 45 degrees.

Edwin</pre>```