Question 159240: Work the following problems and determine if the line is Parallel, Perpendicular, or neither:
l1 : -3y = 24x + 6
l2 : x-8y = -12
Found 2 solutions by checkley77, midwood_trail:
Answer by checkley77(12844)   (Show Source):
You can put this solution on YOUR website! l1 : -3y = 24x + 6
y=24x/-3+6/-3
y=-8x+2 (red line) this line has a slope=-8
l2 : x-8y = -12
-8y=-x-12
y=-x/-8-12/-8
y=x/8+3/2 (green line) this line has a slope=1/8.
Therefore these lines are perpendicular to each other.
 (graph 300x300 pixels, x from -10 to 10, y from -10 to 10, of TWO functions -8x +2 and -x/8 +3/2).
Answer by midwood_trail(310) (Show Source):
You can put this solution on YOUR website! Work the following problems and determine if the line is Parallel, Perpendicular, or neither:
l1 : -3y = 24x + 6
l2 : x-8y = -12
If two lines are parallel, then they have equal slopes.
If two lines are perpendicular, then they have negative reciprocal slopes.
In order to do this, we need to work with two lines.
We solve for y in BOTH equations.
-3y = 24x + 6
y = (24x + 6)/-3
y = -8x - 2....Let's call this guy Equation A.
Do you see the number in front of x? That is the slope. In other worss, the slope of Equation A is -8, which is really -8/1.
What about the other equation?
x - 8y = -12
Again, we isolate y.
Subtract x from both sides.
-8y = -x - 12
We now divide both sides by -8.
y = (-x - 12)/-8
y = (1/8)(x) + (12/8)....Let's call this guy Equation B.
Do you see the fraction in front of x?
That is the slope of this equation. Our slope in Equation B is 1/8.
Notice that we have two slopes:
-8/1 and 1/8
REMEMBER THIS FACT: Any number by itself is really over 1.
So, -8 = -8/1
The opposite of -8/1 = 1/8
The conclusion: These two lines are perpendicular to each other.
Did you follow?
If not, write back.
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