SOLUTION: state the equation of the line parallel to y=3/4X-2 and through (5,-1) into standard form

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Question 37954: state the equation of the line parallel to y=3/4X-2 and through (5,-1) into standard form
Found 2 solutions by Paul, junior403:
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Parallel slope is 3x%2F4
In y=mx+b, y=-1, x=5, and m=3%2F4
-1=%283%285%29%2F4%29%2Bb
-1=15%2F4%2Bb
-1-15%2F4=b
-19%2F4=b
y=2x%2F4-19%2F4
-2x%2F4%2By%2B19%2F4=0
2x-4y-19=0
Hence, the equation is 2x-4y-19=0
Paul.

Answer by junior403(76) About Me  (Show Source):
You can put this solution on YOUR website!
state the equation of the line parallel to y=3/4X-2 and through (5,-1) into standard form.
To find the equation of a line, given the equation of a parallel line
y+=+%283%2F4%29x+-2
and a given point, (5,-1) as (x1,y1)
we can use the point-slope formula...
y+-+y1+=+m%28x+-+x1%29
Now we substitute the given quantities.
NOTE: the slope (m) of a parallel line is equal to the slope (m)
of the original equation.
So...
y+-+%28-1%29+=+%283%2F4%29%28x+-+5%29+-2
Then perform the indicated operations...
y+%2B+1+=+%283%2F4%29x+-+%2815%2F4%29+-2
Now we can subtract (1) to both sides of the equation...
y+=+%283%2F4%29x+-+%2815%2F4%29+-3
Then we can multipy bothsides by the LCD (4) in order to eliminate the fractions.
4%28y%29+=+%284%29%283%2F4%29x+%284%29-+%2815%2F4%29+-3
and we get...
4y+=+3x+-+18
This is our parallel equation,
Now we need to put it in standard form Ax+%2B+By+=+C
So we subtract 3x from both sides...
-3x+%2B+4y+=+-18
Or...
3x+-+4y+=+18
This is your answer.
I hope this helps.
Good Luck!