Question 1062203
Write the point slope form of the equation of the 
horizontal line that passes through the point (2,1)
<pre><font size=4><b>

Let's plot the point (2,1):

{{{drawing(300,300,-5,5,-5,5,graph(300,300,-5,5,-5,5),
locate(2,1,"(2,1)"),

circle(2,1,.05) )}}}

Next let's draw a horizontal line through it (in green):

{{{drawing(300,300,-5,5,-5,5,graph(300,300,-5,5,-5,5),
locate(2,1,"(2,1)"),green(line(-6,1,6,1)),

circle(2,1,.05) )}}}

Now let's plot another point on that line, say the point
(-3,1)

{{{drawing(300,300,-5,5,-5,5,graph(300,300,-5,5,-5,5),
locate(2,1,"(2,1)"),green(line(-6,1,6,1)),
locate(-3,1,"(-3,1)"),
circle(-3,1,.05),
circle(-3,1,.06) )}}}

Now we use the slope formula:

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

{{{m}}}{{{""=""}}}{{{((1)-(1))/((2)-(-3))}}}

{{{m}}}{{{""=""}}}{{{(1-1)/(2+3)}}}

{{{m}}}{{{""=""}}}{{{0/5}}}

{{{m}}}{{{""=""}}}{{{0}}}

Now use the slope-intercept form:

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

{{{y-1}}}{{{""=""}}}{{{0(x-2)}}}

{{{y-1}}}{{{""=""}}}{{{0}}}

{{{y}}}{{{""=""}}}{{{1}}}

A much easier way is just to observe that every point
on that horizontal line will have the same y-coordinate,
so since the point (2,1) has the y-coordinate 1, that means
all values of y on this line will also be 1.  So we could
just have written down the equation

y = 1

in the beginning in one step!!!

Edwin</pre><b></pre></b>