document.write( "Question 1200345: How do you know where to graph these two equations?
\n" ); document.write( "3y-2x=6 and -12y+8x=-24\r
\n" ); document.write( "\n" ); document.write( "In the textbook, it says that both equations have a y-intercept of (0,2) but I am not understanding HOW they got that? \n" ); document.write( "

Algebra.Com's Answer #834451 by ikleyn(52878) $\"\"$ $\"About$

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\n" ); document.write( "How do you know where to graph these two equations?
\n" ); document.write( "3y-2x=6 and -12y+8x=-24
\n" ); document.write( "In the textbook, it says that both equations have a y-intercept of (0,2)
\n" ); document.write( "but I am not understanding HOW they got that?
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document.write( "My explanation consists of two positions.\r\n" );
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document.write( "(1)  The equations are\r\n" );
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document.write( "         3y - 2x =   6    (1)\r\n" );
document.write( "       -12y + 8x = -24    (2)\r\n" );
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document.write( "     Multiply the first equation by (-4).  You will get an equivalent equation\r\n" );
document.write( "     and an equivalent system\r\n" );
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document.write( "        -12y + 8x = -24    (1')\r\n" );
document.write( "        -12y + 8x = -24    (2')\r\n" );
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document.write( "     Now you see that both equations are identical.  Hence, they represents \r\n" );
document.write( "     the SAME STRAIGHT LINE on the coordinate plane.\r\n" );
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document.write( "     Again: both equations (1'), (2') represent one line.\r\n" );
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document.write( "     HENCE, the original equations (1), (2) represent THE SAME unique line.\r\n" );
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document.write( "(2)  Now, the point (0,2) is the solution to both equations (1') and (2').\r\n" );
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document.write( "     You can CHECK it by substituting  x= 0, y= 2 into equations (1') and (2').\r\n" );
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document.write( "     But since the point (0,2) is the y-intersection (since x= 0 in it (!) ),\r\n" );
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document.write( "     you obtain the ANSWER : the point (0,2) is y-interception to both equations that represent the same line.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "From my explanation, you learned two facts\r
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\n" ); document.write( "\n" ); document.write( " - (1) that the equations represent the same straight line, and\r
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\n" ); document.write( "\n" ); document.write( " - (2) that the point (0,2) is y-interseption of this line.\r
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\n" ); document.write( "\n" ); document.write( "You also learned HOW to discover/(to establish) this fact: simply substitute
\n" ); document.write( "x= 0, y= 2 into equation/equations and make sure that it is a solution to the given equation.\r
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\n" ); document.write( "\n" ); document.write( "Now, since the point (0,2) with x= 0 lies on the line, it $\"highlight%28highlight%28IS%29%29\"$ y-interception.\r
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