Question 113775
 We are going to calculate {{{the }}}{{{change}}} in {{{y}}} over {{{the }}}{{{change}}} in{{{ x}}},or the {{{rise}}} over the{{{ run}}}. 

Here are examples for your lines:


Find the slope of the straight line that passes through ({{{x[1]}}}, {{{y[1]}}}) and ({{{x[2]}}}, {{{y[2]}}}) or state that the slope is undefined.  Then indicate if the line through the points:

{{{rises}}} (left to right), ……………this will be in case when {{{slope }}} has positive value

{{{falls }}}(left to right),  ……………this will be in case when {{{slope }}} negative value

is {{{horizontal}}}, ……………this will be in case when {{{slope }}} is equal to {{{0}}}

or is {{{vertical}}}……………. this will be in case when {{{slope }}} is undefined
 
1.
If  the straight (for example)line that passes through (4,1) and (-2,1),then slope is:

{{{m = rise/run}}}

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

Plug in {{{x}}} and {{{y }}}values into slope formula

{{{m = (1-1)/(4-(-2))}}}

{{{m = (1-1)/(4+2)}}}………….. Simplify

{{{m = 0/6}}}

{{{m = 0}}}

The slope of the line is {{{0}}}. 
Since the {{{slope}}}{{{ is}}}{{{ zero}}}, the {{{line}}} would be {{{horizontal}}}.


2.

  
If  the straight line that passes through (-2, 3) and (-2, 5)  
  
 {{{m = rise/run}}}

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

Plug in {{{x}}} and {{{y }}}values into slope formula

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

{{{m = (-2)/(-2+2)}}}………….. Simplify

{{{m = -2/0}}}

The slope of the line is {{{undefined}}}. 
Since the {{{slope}}} is{{{ undefined}}}, the {{{line}}} would be {{{vertical}}}.

3.
  
find the slope going from (-2,0) to (-1,-2)
  

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

Plug in {{{x}}} and {{{y }}}values into slope formula

{{{m = (-2-0)/(-1-(-2))}}}

{{{m = -2/1}}}………….. Simplify

{{{m = -2}}}


  
 4.
find the slope passing through (1,0) to (-1,1)

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

Plug in {{{x}}} and {{{y }}}values into slope formula

{{{m = (1-0)/(-1-(-2))}}}

{{{m = 1/1}}}………….. Simplify

{{{m = 1}}}