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Question 117568: which line is parallel to the line y=4x-2
a. 12x-4y=8
b. 4y-16x=10
c. 5y-25x=-10
d. -x+4y=-8
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The answer to this problem is choice b. But how do you find that answer to be correct.
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Recognize two things. First, if two lines are parallel, they have the same slope.
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Second, if you have an equation of the form y = mx + b, then m (the multiplier of x) is the slope
of the line represented by that equation.
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You are given the line y = 4x - 2. From this you can tell that the slope of this line is +4
because +4 is the multiplier of x. [You can also tell that the graph crosses the y-axis at the
point where y = -2, but you don't need to know that for this problem.]
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Now all you have to do is rearrange each of the equations in the four choices to find their slopes.
When you find the equation with the multiplier of x equal to +4 then you will know that
it represents the line that is parallel to the given equation.
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Do answer a.
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Given 12x - 4y = 8
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Subtract 12x from both sides to get:
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-4y = -12x + 8
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Divide both sides (all terms) by -4 to solve for y and you have:
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y = 3x - 2
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In this equation the multiplier of x is +3 not +4. So it does not represent a parallel line.
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Do answer c.
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Given 5y - 25x = -10
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Add +25x to both sides to get rid of the -25x on the left side and you have:
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5y = 25x - 10
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Solve for y by dividing both sides (all terms) by +5 and you have:
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y = 5x - 2
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The slope of the line represented by this equation is 5 and therefore it cannot be parallel either.
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Do answer d.
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Given -x + 4y = -8
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Get rid of the -x on the left side by adding x to both sides to make the equation become:
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4y = +x - 8
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Solve for y by dividing both sides (all terms) by 4 and you have:
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y = (1/4)x - 2
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This cannot be parallel because its slope is +(1/4)
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Finally do answer b
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Given 4y - 16x = 10
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Get rid of the -16x on the left side by adding +16x to both sides to get:
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4y = 16x + 10
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Solve for y by dividing both sides (all terms) by +4 and the equation becomes:
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y = 4x + 10/4
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The slope (the multiplier of x) is +4, the same as the slope of the equation you were originally
given. Therefore, this line is parallel to the given line. Answer b is the correct answer.
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Hope this helps you to see how to do the problem.
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