Question 225476: Please help me tell whether the lines are "parallel,perpendicular,or neither". f(x)=y
f(x)=2x-4
8x+4f(x)=8
Answer by drj(1380)   (Show Source):
You can put this solution on YOUR website! Please help me tell whether the lines are "parallel,perpendicular,or neither". f(x)=y
f(x)=2x-4 or y=2x-4 where y=f(x)
8x+4f(x)=8 or 4y=-8x-8 where y=f(x)
Step 1. Line are parallel when they have the same slope and lines are perpendicular when the product of the slopes between the two lines is -1 or m1*m2=-1 where m1 is the slope of the first line and m2 is the slope of the perpendicular line.
Step 2. Let's put the equations in slope intercept form where y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b)
Step 3. Here, y=2x-4 is in slope intercept form so it has a slope of 2.
Step 4. Now 4y=8x-8 can be put in slope intercept form where we can divide by 4 to both sides of the equation giving y=-2x-2. So the slope is -2.
Step 5. The slopes in Step 3 and 4 are not equal so it's not parallel and their product is not -1 so they are not perpendicular.
Step 6. ANSWER: Based on the Steps 3-5, the lines are neither parallel nor perpendicular.
I hope the above steps were helpful.
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Good luck in your studies!
Respectfully,
Dr J
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