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April 16th, 2013, 09:55 PM  #1 
Newbie Joined: Apr 2013 Posts: 2 Thanks: 0  Linear Equations
find the equation of a line parallel to 3x + 4y = 8 with the same yintercept as 5x  3y = 10 Find the equation of a line parallel to 2x +7y = 10 with the same xintercept as 3x  4y = 5 
April 17th, 2013, 04:31 AM  #2 
Member Joined: Jan 2012 Posts: 80 Thanks: 0  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. 
April 17th, 2013, 05:37 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 17,221 Thanks: 1294 
To find the yintercept 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 yintercept (0, 10/3) is 3x + 4y = 40/3, or 9x + 12y = 40. 
April 17th, 2013, 01:21 PM  #4 
Newbie Joined: Apr 2013 Posts: 2 Thanks: 0  Re: Linear Equations
How would you find the xintercept though? I figured out how to do the first question

April 17th, 2013, 10:07 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 17,221 Thanks: 1294 
To find the yintercept for 3x  4y = 5, one puts y = 0 and solves for x, getting x = 5/3.


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