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Question 576060: Are the following two lines parallel? 3x + 4y = 4 2x - 6y = 7
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! In order to be parallel, the graphs of each of these two equations must have the same slope.
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To find the slopes, let's convert each equation to the slope intercept form. That form is:
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y = mx + b
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and m, which is the multiplier of x, is the slope of the graph. (b is the value at which the graph crosses the y-axis.)
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So let's look at the first equation and let's solve it for y.
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Start with:
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3x + 4y = 4
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Get rid of the 3x on the left side by subtracting 3x from both sides. With that subtraction the equation becomes:
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4y = -3x + 4
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Now solve for y by dividing both sides of this equation (all terms) by 4. This results in:
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y = (-3/4)x + 4/4
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and the 4/4 results in 1, so the equation becomes:
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y = (-3/4)x + 1
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By comparing this to the slope intercept form you can see that m, the slope, is the multiplier of x and it is -3/4.
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Now, lets do the same thing for the second equation.
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Start with:
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2x - 6y = 7
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Get rid of the 2x on the left side by subtracting 2x from both sides to get:
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-6y = -2x + 7
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Solve for y by dividing both sides (all terms) by -6 and the equation becomes:
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y = (-2/-6)x + 7/(-6)
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This time the multiplier of the x is (-2/-6) which reduces to +1/3. ( b is equal to -7/6)
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So for one equation we have the slope equal to -3/2 and for the other equation the slope is +1/3. The two slopes are not the same. Therefore, the graphs have to cross somewhere. And since they cross at some point they are not parallel.
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You now have the answer and there is nothing else that you need to do.
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Hope this helps you to understand the problem.
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