document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166611>Question 166611</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How to determine if the equations are parallel, Perpendicular or neither ?\r<BR>\n" );
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document.write( "1. y + 3 = 6x<BR>\n" );
document.write( "   -6x + y = 4\r<BR>\n" );
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document.write( "2. 3y + 21 = 2x<BR>\n" );
document.write( "   2y = 10 - 3x\r<BR>\n" );
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document.write( "3. y = -x + 8<BR>\n" );
document.write( "   -2x -y = 4 </SPAN>\n" );
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document.write( "1. y + 3 = 6x<BR>\n" );
document.write( "-6x + y = 4 <BR>\n" );
document.write( "2. 3y + 21 = 2x<BR>\n" );
document.write( "2y = 10 - 3x <BR>\n" );
document.write( "3. y = -x + 8<BR>\n" );
document.write( "-2x -y = 4<BR>\n" );
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document.write( "Find the slope (m) of each line.  If the slope is the same, they're parallel.  If the slopes are negative inverses (m and -1/m), they're perpendicular.  Otherwise, they're neither.<BR>\n" );
document.write( "1. y + 3 = 6x<BR>\n" );
document.write( "-6x + y = 4 <BR>\n" );
document.write( "Put into slope-intercept form, y = mx + b<BR>\n" );
document.write( "y = 6x - 3<BR>\n" );
document.write( "y = 6x + 4<BR>\n" );
document.write( "Slope is 6 in both, so they're parallel.<BR>\n" );
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document.write( "2. 3y + 21 = 2x<BR>\n" );
document.write( "2y = 10 - 3x <BR>\n" );
document.write( "The coefficient term can be ignored for these problems.<BR>\n" );
document.write( "3y + 21 = 2x   m = 2/3<BR>\n" );
document.write( "2y = 10 - 3x   m = -3/2  Perpendicular<BR>\n" );
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document.write( "3. y = -x + 8  m = -1<BR>\n" );
document.write( "-2x -y = 4     m = -2  Neither\r<BR>\n" );
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document.write( " </SPAN>\n" );
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