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How to determine if the given lines are parallel, perpendicular or neither?

I was sick for four days and my teachers gave me notes that were not filled out and expects me to understand what I’m doing. Please help!

Tell whether the lines are parallel , perpendicular or neither. y=4x+5 and y=1/4x+4
Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the give line. (-3,1); y=1/3x+2
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the given line. (-6,4); y=3/2x+2

I don’t need you to do my homework for me, if anything I need this to be explained to me. I just gave you some examples, if someone could please help me with what the heck I’m doing, it would be greatly appreciated.

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Answer #1

If they are parralell, the slopes are the same, which is the ‘m’ in y=mx+b. If it is perpendicular, then they have a negative reciprocal slope, meaning one is 4 the other is -1/4. For the question, you already have the slopes you just have to see if it fits into any of the categories if not it is neither. As for the other two, using the point you were given, substitute it into “x” abd “y” in the y=mx+b equation, and then solve for ;’m’, or the slope. Then with the number you got for the slope, compare with the slope with the equation you were given, and determine from there.

Answer #2

parallel is having the SAME slope. perpendicular has a opposite reciprocal slope. a parallel slope of 2 is 2. a perpendicular slope of 2 is -1/2. hope this helpsss

Answer #3

Thank you so much!

Answer #4

No problem :}

Answer #5

parallel is like this ll perpendicular is -l

Answer #6

for 2 lines to be perpendicular the multiplication of slopes of both of them will be -1 i.e m1m2=-1 if the lines are parallel then the slope of both the equations will be equal. m1=m2

Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the give line. (-3,1); y=1/3x+2

see here the slope is 1/3 m1*1/3=-1 m1=-3 now the equation of line will be y=-3x+c given that the line pass (-3,1) 1=-3(-3)+c 1-9=c c=-8 or the equation will be y=-3x-8

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How to determine if the given lines are parallel, perpendicular or neither?

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