SOLUTION: Two lines are parallel if and only if they have the same slop. Complete the equation of the line that is parallel to the line with the equation y=2x+5 and that passes through the

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Question 914953: Two lines are parallel if and only if they have the same slop. Complete the equation of the line that is parallel to the line with the equation y=2x+5 and that passes through the point (2,1).
y=mx+b
What is the correct value of m?
Found 2 solutions by ewatrrr, Edwin McCravy:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Rule: the standard slope-intercept form for an equation of a line is
y+=+highlight_green%28m%29x+%2B+highlight%28b%29 where m is the slope and b the y-intercept.
y+=+highlight_green%282%29x+%2B+highlight%285%29, m = 2
.......
New Line Using point-slope form, y+-+y%5B1%5D+=+m%28x+-+x%5B1%5D%29P(2,1)
y - 1 = 2(x-2)
y - 1 = 2x - 4
y = 2x - 3

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
She did it using the point-slope form.  I'll do it using
only the slope-intercept form y = mx+b


y = 2x+5

compare that to

y = mx+b

And see that the slope is m=2 and the y-coordinate of the y-intercept
is b=5, and so the y-intercept is (0,5), but you only need the slope

The slope of any line parallel to it will also have slope m=2 but
will have a different value for b.  So substitute b=2 in

 y = mx+b

and get

 y = 2x+b

Then since it goes through the point (2,1) we substitute x=2 and y=1

 1 = 2(2)+b

 1 = 4+b
-3 = b

Now substitute -3 for b in

 y = 2x+b

and get:

 y = 2x-3

Edwin