SOLUTION: HELP WITH ALGEBRAIC PROBLEMS!!! Write the equation of a line parallel to the given line but passing through the given point. y=1/4x-2;(8,-1). Write the equation of a line p

Algebra ->  Graphs -> SOLUTION: HELP WITH ALGEBRAIC PROBLEMS!!! Write the equation of a line parallel to the given line but passing through the given point. y=1/4x-2;(8,-1). Write the equation of a line p      Log On


   

Question 969250: HELP WITH ALGEBRAIC PROBLEMS!!!
Write the equation of a line parallel to the given line but passing through the given point.
y=1/4x-2;(8,-1).
Write the equation of a line perpendicular to the given line but passing through the given point.
y=-4x-5;(0,-1)
Can you please show the steps through out the whole process? I am not sure how to do this without coming up with different answers each time.
Found 3 solutions by stanbon, Fombitz, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Write the equation of a line parallel to the given line but passing through the given point.
y=1/4x-2;(8,-1).
----
The given equation has slope = 1/4.
Any line parallel to it must have slope = 1/4
----
Form of your equation:
y = mx + b
Solve for "b"::
-1 = (1/4)8 + b
-1 = 2 + b
b = -3
---
Ans: y = (1/4)x - 3
-----------------------------
Write the equation of a line perpendicular to the given line but passing through the given point.
y=-4x-5;(0,-1)
The given equation has slope = -4
Any line perpendicular to it must have slope = 1/4
Form::
y = mx + b
Solve for "b"::
-1 = (1/4)*0 + b
b = -1
Ans: y = (1/4)x - 1
---------------
Cheers,
Stan H.
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Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Parallel lines have identical slopes.
m=1%2F4
Use the point-slope form with the point.
y-%28-1%29=%281%2F4%29%28x-8%29
y%2B1=%281%2F4%29x-2
y=%281%2F4%29x-3
.
.
.
.
.
.
.
Perpendicular lines have slopes that are negative reciprocals.
m%5B1%5D%2Am%5B2%5D=-1
-4%2Am%5B2%5D=-1
m%5B2%5D=1%2F4
Again, point slope form,
y-%28-1%29=%281%2F4%29%28x-0%29
y%2B1=%281%2F4%29x
y=%281%2F4%29x-1
.
.
.
.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
++y+=+%281%2F4%29%2Ax+-+2+
(8, -1 )
Any line parallel to the given line must
have slope = +1%2F4+
-----------------------
Use general point-slope formula
+%28+y+-%28+-1+%29+%29+%2F+%28+x+-+8+%29+=+1%2F4+
+%28+y+%2B+1+%29+%2F+%28+x+-+8+%29+=+1%2F4+
Multiply both sides by +4%2A%28+x+-+8+%29+
+4%2A%28+y+%2B+1+%29+=+x+-+8+
+4y+%2B+4+=+x+-+8+
+4y+=+x+-+12+
+y+=+%28+1%2F4+%29%2Ax+-+3+
-----------------
check:
does it go through ( 8, -1 ) ?
++-1+=+%28+1%2F4+%29%2A8+-+3+
+-1+=+2+-+3+
+-1+=+-1+
OK
==========================
+y+=+-4x+-+5+
( 0,-1 )
Any line perpendicular to the given
line will have slope =
+m+=+-1+%2F+%28+-4+%29+
+m+=+1%2F4+
---------------
Use general point-slope formula
+%28+y+-%28+-1+%29+%29+%2F+%28+x+-+0+%29+=+1%2F4+
+%28+y+%2B+1+%29+%2F+x+=+1%2F4+
Multiply both sidesby +4x+
+4%2A%28+y+%2B+1+%29+=+x+
+4y+%2B+4+=+x+
+4y+=+x+-+4+
+y+=+%28+1%2F4+%29%2Ax+-+1+
---------------------
check:
does it go through ( 0, -1 ) ?
+-1+=+%28+1%2F4+%29%2A0+-+1+
+-1+=+-1+
OK