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Question 83787: HI my homework says to " write the equation of the line in slope-intercept form:
parallel to -5y=10x+32 and through point P(-1,1). Can you clear things up for me? I am completley lost, and there is nothing in my textbook on this, or maybe i am just overlooking it.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! For lines to be parallel, they must have the same slope.
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You are given the equation:
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-5y=10x+32
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You can find the slope of the graph of this equation by "rearranging" the given equation
into the slope intercept form of y = mx + b. [In this form m (the multiplier of x] is the
slope and b is the value on the y-axis where the graph crosses (or intercepts).
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So we need to solve the given equation for y. If we do that, the resulting equation
will be in the slope intercept form. Since the given equation has -5y, we can find y
by dividing all terms on both sides by -5, the multiplier of y. Dividing by -5 results in:
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y = (10/-5)x + (32/-5)
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The division causes the coefficient [or multiplier] of x to become -2 and the resulting
equation is:
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y = -2x - (32/5)
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Since this is in slope intercept form, we now know that the graph of the given equation
crosses the y-axis at -32/5 and the graph has a slope of -2 (it goes vertically down 2
units every time it moves horizontally to the right 1 unit).
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Since the line we are looking for is now known to have a slope of -2 (it must have the
same slope as the given line to be parallel), we can now write part of the slope intercept
form of the equation of this new line. The new line will be of the form:
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y = -2x + b
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The problem tells you that this line must go through the point (-1,1) which means that
the equation must be true when x = -1 and y = +1.
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So we can substitute these values for x and y in the equation of the new line. Therefore,
substitute these values into:
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y = -2x + b
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and you get:
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1 = -2(-1) + b
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Multiply out the first term on the right side and you get:
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1 = 2 + b
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Solve for b by subtracting 2 from both sides of the equation to get:
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1 - 2 = 2 - 2 + b
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which simplifies to:
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-1 = + b
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We now know that b = -1 so our equation for the new line becomes:
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y = -2x + b
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and by substituting -1 for b it is:
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y = -2x - 1
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That's the answer. And if you graphed the original equation and this new equation,
the graph would look like this:
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in which the green line (which crosses the y-axis at -1) represents the parallel line that
we found, and the other line is the graph of the equation you were originally given.
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Hope this helps you to understand the process of making a parallel line. Remember
that the slopes of the two lines must be the same.
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