Question 152294
Hi, Hope I can help
.
Determine the slope of the line that passes through each pair of points.
1.(5,1) and (2,7) 
2.(5,3)and(-2,3) 
3.({{{-1/2}}},-2)and({{{-3/2}}},1) 
4.(2,-4)and(2,6)
.
The First Points in our problem( (5,1) , (5,3) , ( {{{ -1/2 }}},-2), and (2,-4))
will be (x1,y1) ( In (5,1) 5 = x1, 1 = y1 )
.
The Second Points in our problem( (2,7) , (-2,3) , ( {{{ -3/2 }}},1), and (2,6))
will be (x2,y2) ( In (2,6) 2 = x2, 6 = y2 )
.
The equation to find the slope is {{{ (y2-y1)/(x2-x1) }}}
.
We can now find the slope in each problem, we will do them one at a time
.
Find the slope of a line that passes through (5,1) and (2,7)
.
(5,1) (x1,y1) and (2,7) (x2,y2)
.
Our equation is {{{ (y2-y1)/(x2-x1) }}}, we can replace the letters with numbers
.
{{{ (y2-y1)/(x2-x1) }}} = {{{ (7-1)/(2-5) }}}
.
{{{ (7-1)/(2-5) }}} = {{{ (6)/(-3) }}}
.
{{{ (6)/(-3) }}} = {{{ -2/1 }}}, or (-2)
.
The slope of a line that passes through (5,1) and (2,7) is = (-2)
.
Now we will solve our second slope
.
Find the slope of a line that passes through (5,3)and(-2,3)
.
(5,3) (x1,y1) and (-2,3) (x2,y2)
.
We can switch the two points, and we can still find the slope
.
(-2,3)(x1,y1) and (5,3) (x2,y2) 
.
( the letters don't change, The first point in a pair will always be (x1,y1), the second point will always be (x2,y2))
.
(5,3) (x1,y1) and (-2,3) (x2,y2)
.
equation = {{{ (y2-y1)/(x2-x1) }}}, we will replace letters with numbers
.
{{{ (y2-y1)/(x2-x1) }}} = {{{ (3 - 3)/((-2) - 5) }}}
.
{{{ (3 - 3)/((-2) - 5) }}} = {{{ 0/ -7 }}}, or "0"
.
 The slope of a line that passes through (5,3)and(-2,3) is = "0"
.
We will solve the third slope
.
Find the slope of a line that passes through ({{{-1/2}}},-2)and({{{-3/2}}},1)
.
({{{-1/2}}},-2)(x1,y1) and ({{{-3/2}}},1) (x2,y2)
.
equation = {{{ (y2-y1)/(x2-x1) }}}, we will replace letters with numbers
.
{{{ (y2-y1)/(x2-x1) }}} = {{{ (1 - (-2))/((-3/2)-(-1/2)) }}}
.
{{{ (1 - (-2))/((-3/2)-(-1/2)) }}} = {{{ 3 /(-1) }}}, or (-3)
.
The slope of a line that passes through ({{{-1/2}}},-2)and({{{-3/2}}},1) is = (-3)
.
We will now solve our last slope
.
Find the slope of a line that passes through (2,-4)and(2,6)
.
(2,-4) (x1,y1) and (2,6) (x2,y2)
.
Our equation = {{{ (y2-y1)/(x2-x1) }}}, we will replace the letters with numbers
.
{{{ (y2-y1)/(x2-x1) }}} = {{{ (6-(-4))/(2-2) }}}
.
{{{ (6-(-4))/(2-2) }}} = {{{ 10 / 0 }}}, or "no slope"( you can't divide a number by "0")
.
The slope of a line that passes through (2,-4)and(2,6) is = "no slope"
.
The four slopes are
.
1.(5,1) and (2,7)       (slope = (-2))
2.(5,3)and(-2,3)        (slope = "0")
3.({{{-1/2}}},-2)and({{{-3/2}}},1)  (slope = (-3))
4.(2,-4)and(2,6)        (slope = "no slope")
.
Hope I helped, Levi