SOLUTION: I need help in writing equations for lines that are parallel to a given line and passes through a given point. For example: 4y-5=2x ; (-3,-2)

Algebra ->  Linear-equations -> SOLUTION: I need help in writing equations for lines that are parallel to a given line and passes through a given point. For example: 4y-5=2x ; (-3,-2)      Log On


   

Question 281612: I need help in writing equations for lines that are parallel to a given line and passes through a given point. For example:
4y-5=2x ; (-3,-2)
Found 2 solutions by josmiceli, Mathematicians:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You have to get the equation into the
form y+=+mx+%2B+b, where m = slope
4y+-+5+=+2x
Add 5 to both sides
4y+=+2x+%2B+5
divide both sides by 4
y+=+%281%2F2%29%2Ax+%2B+5%2F4
Any line parallel to this line will have slope = 1%2F2
So far I have y+=+%281%2F2%29%2Ax+%2B+b, and all I need is b
The line must pass through (-3,-2), so I can just plug
these values in and solve for b
-2+=+%281%2F2%29%2A%28-3%29+%2B+b
Multiply both sides by 2
-4+=+-3+%2B+2b
Add 6 to both sides
2b+=+-1
b+=+-1%2F2
The solution is y+=+%281%2F2%29%2Ax+-+1%2F2
check:
does it go through (-3,-2)?
-2+=+%281%2F2%29%2A%28-3%29+-+1%2F2
-2+=+-3%2F2+-+1%2F2
-2+=+-2
OK

Answer by Mathematicians(84) About Me  (Show Source):
You can put this solution on YOUR website!
4y+-+5+=+2x
we need to find the slope from the above equation, in order to do that, we want to put it in:
y+=+mx+%2B+b form
4y+-+5+=+2x add 5 to both sides
4y+=+2x+%2B+5 divide 4 on both sides
y+=+1%2F2%2Ax+%2B+5%2F4
the coefficient of x is 1%2F2, so our slope is 1%2F2
From there, we can use this formula to find the equation of the line parallel to the point (-3,-2)
Y+-+y+=+m%28X+-+x%29 where lowercase y and x is from the point and m is slope.
Y+-+%28-2%29+=+1%2F2+%28X+-+%28-3%29%29 distribute the 1/2
Y+%2B+2+=+1%2F2+%2A+X+%2B+3%2F2 subtract 2 on both sides
highlight%28Y+=+1%2F2+%2A+X+-+1%2F2%29 final answer