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April 16th, 2013, 09:55 PM   #1
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Linear Equations

find the equation of a line parallel to 3x + 4y = 8 with the same y-intercept as 5x - 3y = 10

Find the equation of a line parallel to 2x +7y = 10 with the same x-intercept as 3x - 4y = 5
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April 17th, 2013, 04:31 AM   #2
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Re: Linear Equations

Hi Blaze,

You need to find the gradient of the line you want the new line to be parallel to. So you need to rearrange to the form (m is the gradient):







The gradient of this line is .

Now you need to find the y intercept of the other line. Again you need to rearrange to the form (c is the y intercept):







The y intercept of this line is .

Now you can use that gradient and y intercept to give the equation for the new line:



You should be able to apply the same steps to work out the second question.
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April 17th, 2013, 05:37 AM   #3
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To find the y-intercept for 5x - 3y = 10, one puts x = 0 and solves for y, getting y = -10/3.
Substituting (x, y) = (0, -10/3) into 3x + 4y gives -40/3.
Hence the line parallel to 3x + 4y =8 with y-intercept (0, -10/3) is 3x + 4y = -40/3, or 9x + 12y = -40.
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April 17th, 2013, 01:21 PM   #4
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Re: Linear Equations

How would you find the x-intercept though? I figured out how to do the first question
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April 17th, 2013, 10:07 PM   #5
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To find the y-intercept for 3x - 4y = 5, one puts y = 0 and solves for x, getting x = 5/3.
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