Question 67258
WRITE THE EQUATION of the line passing throiugh the given points:
(-1, 3)and (4, -2)
In order to write the equation of a line, you need a slope and a point.  
We have two points, therefore we can use the slope formula to find the slope:  {{{highlight(m=(y2-y1)/(x2-x1))}}}, m=slope, and (x1,y1) and (x2,y2) are given points.
(x1,y1)=(-1,3) and (x2,y2)=(4,-2)
{{{m=(-2-3)/(4-(-1))}}}
{{{m=-5/5}}}
{{{m=-1}}}
Now that we have a slope and a point we can use the point slope formula to find the equation of the line:   {{{highlight(y-y1=m(x-x1))}}}, m=slope and (x1,y1) is a given point.
m=-1 and (x1,y1)=(-1,3)
{{{y-3=-1(x-(-1))}}}
{{{y-3=-1(x+1)}}}
{{{y-3=-x-1}}}
{{{y-3+3=-x-1+3}}}
{{{highlight(y=-x+2)}}}
This is not the only way to do this, let me know if your book is doing something a little different.
:
(2, -3) and (2,4)
This is a special case, notice that the two x's are the same.  If you were to plot these two points and connect the points, you would find you had a vertical line going through x=2.  
The equation of a vertical line going through x=2, is:
{{{highlight(x=2)}}}
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FYI, The other special case would be if the y's were the same, then the equation would be y=k, where k is their matching y value. 
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Happy Calculating!!!!