Question 81637
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I'm learning how to write my "results" in 
slope-intercept form. And I'm having a little
difficulty trying to get these worked out and 
was wondering if I could get some assistance. 

(0,5), m = {{{-3/5}}} 

Substitute in the point slope formula:

   y - y<sub>1</sub> = m(x - x<sub>1</sub>)

where x<sub>1</sub> = 0 and y<sub>1</sub> = 5

   y - 5 = {{{-3/5}}}(x - (0) )

   y - 5 = {{{-3/5}}}x

       y = {{{-3/5}}}x + 5

That's the equation in the slope-intercept
form because we can compare it with

       y = mx + b

and see that its slope m is {{{-3/5}}} and its
y-intercept (0,b) is the point (0,5)

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1. (-1, 3) and (4,-2)

We first plot those two points and draw a line 
through them to find out if it is vertical or
not. The equations of all lines can be placed
in slope-intercept form except the equations
for vertical lines. This is the graph we get:

{{{graph( 300, 300, -5, 5, -5,5,  -x + 2)}}}

We see that it is not vertical. So we can proceed
as usual:

We are to find an equation of the line containing 
the points (-1,3) and (4,-2)

Use the slope formula:

     y<sub>2</sub> - y<sub>1</sub>
m = —————————
     x<sub>2</sub> - x<sub>1</sub>

where (x<sub>1</sub>, y<sub>1</sub>) = (-1,3) and (x<sub>2</sub>, y<sub>2</sub>) = (4, -2)

    (-2) - (3)    -5      -5
m = —————————— = ————— = ———— = -1
    (4) - (-1)    4+1      5 

Now substitute in the point slope formula:

   y - y<sub>1</sub> = m(x - x<sub>1</sub>)

   y - 3 = (-1)(x - (-1) )

   y - 3 = -(x + 1)

   y - 3 = -x - 1

       y = -x + 2

That's the equation in the slope-intercept
form because we can compare it with

       y = mx + b

and see that its slope m is -1 and its
y-intercept (0,b) is the point (0,2)
  
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(2,-3) and (2,4) 

We plot those two points and draw a line
through them:

{{{graph(300,300,-6,6,-6,6,9999(x-2))}}}

It is vertical, so we can't go the usual route.
Since vertical lines are the only kind of lines
which don't have slopes, there is no slope-intercept
form.  But we can still write the equation.  It is 
simply this:

       x = 2

because every point on that line has x-coordinate 2.

So x = 2 tells the story of every point on the line,
so that's all there is to the equation of that vertical
line.

Edwin
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