If you rewrite the equation of line A in the form y = (-1/4)x + 3/4, you can see that line A has a slope of -1/4 (when the equation of a line is written in the form y = mx + b, then m is the slope). Parallel lines have the same slope, so the equation of a parallel line will look like y = (-1/4)x + c, where c is some number. There are a lot of different lines which are parallel to A, so we can't produce an exact equation here without more information.nasir wrote:Two lines A and B are parallel
Equation of line A is x= 3-4y
What would be the equation of line B ?
Please explain your answer, if possible include an example too
Thanks in advance.
parallel lines
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Ian Stewart
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tlt2372
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Re-arrange the equation to slope intercept form..
y=-1/4(x)+3/4
The slope of a line parallel to line A has the same slope as line A. So the slope of Line B will be -1/4.
You can use the point slope formula to calculate the equation for Line B. Pick a point that you want Line B to go through.
I chose (0,0)
So y-y1 =m(x-x1) where y1 and x1 are (0,0)
Solving you get y=-1/4x+0
y=-1/4(x)+3/4
The slope of a line parallel to line A has the same slope as line A. So the slope of Line B will be -1/4.
You can use the point slope formula to calculate the equation for Line B. Pick a point that you want Line B to go through.
I chose (0,0)
So y-y1 =m(x-x1) where y1 and x1 are (0,0)
Solving you get y=-1/4x+0
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nasir
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it means, there is only one condition for lines to be parallel and that is " same slope ". InParallel lines have the same slope
y=mx+b What about b ? is it necessary for parallel lines to have different values of b or b
could be same as well ?
Thanks
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tlt2372
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If you have the same slope, represented by m in the slope intercept equation, and the same b, the lines would be on top of one another.nasir wrote:it means, there is only one condition for lines to be parallel and that is " same slope ". InParallel lines have the same slope
y=mx+b What about b ? is it necessary for parallel lines to have different values of b or b
could be same as well ?
Thanks
Ian was right when he said to completely solve this problem, you need a coordinate. I chose (0,0) because it was easy to work with. If you were given a question on the gmat, they would give you another coordinate since there are endless possibilities without one.
Hope this helps
