document.write( "Question 208010This question is from textbook elementary and intermediate algebra
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determine whether each pair of equations represents parallel lines:
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document.write( "There are several ways to do this. Pick whichever way\r\n" );
document.write( "your teacher told you to use.\r\n" );
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document.write( "Method 1:  Put them both in slope-intercept form. If \r\n" );
document.write( "their slopes are equal, but they have different \r\n" );
document.write( "y-intercepts, then they are parallel.\r\n" );
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document.write( "Method 2:  Choose any two values for x.  Substitute \r\n" );
document.write( "           them both in each equation to find the \r\n" );
document.write( "           y-values corresponding to them.  If the \r\n" );
document.write( "           corresponding y-values have the same non-zero\r\n" );
document.write( "           difference, then the lines are parallel.\r\n" );
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document.write( "Method 3:  Put them both in general form. Then \r\n" );
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document.write( "if  then they are parallel.   \r\n" );
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document.write( "Method 1:  \r\n" );
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document.write( "The first one is already in the slope intercept form\r\n" );
document.write( ".  Get the second one in slope-intercept \r\n" );
document.write( "form, by solving for y\r\n" );
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document.write( "Add  to both sides:\r\n" );
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document.write( "Divide every term by :\r\n" );
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document.write( "So the slope is the coefficient of x, which is -3\r\n" );
document.write( "So the value of the slope  is the same in \r\n" );
document.write( "both equations, but their y-intercepts are different.\r\n" );
document.write( "Therefore the lines those equations\r\n" );
document.write( "represent are parallel.\r\n" );
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document.write( "Method 2:\r\n" );
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document.write( "Substitite x=0 in each and solve for y:\r\n" );
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document.write( "In the first one:\r\n" );
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document.write( "In the second one:\r\n" );
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document.write( "Subtract them, second y - first y = \r\n" );
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document.write( "Substitite x=1 in each and solve for y:\r\n" );
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document.write( "In the first one:\r\n" );
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document.write( "In the second one:\r\n" );
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document.write( "Subtract them, second y - first y = \r\n" );
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document.write( "We get the same difference 3, so the lines represented\r\n" );
document.write( "by those equations are parallel.\r\n" );
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document.write( "Method 3:\r\n" );
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document.write( "Get the forst one in general form:\r\n" );
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document.write( "So the system is now:\r\n" );
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document.write( "See if the coefficients of x and y are in\r\n" );
document.write( "the same proportion:\r\n" );
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document.write( "Is  true?\r\n" );
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document.write( "Yes it is, therefore the lines those equations\r\n" );
document.write( "represent are parallel.\r\n" );
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document.write( "Edwin

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