document.write( "Question 208161: graph 3x + 2y = 6. Where do you begin? Explain \n" ); document.write( "
Algebra.Com's Answer #157477 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
There are two ways to do this (actually there are more, but I'm only showing two here).\r
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\n" ); document.write( "\n" ); document.write( "Method #1\r
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\n" ); document.write( "\n" ); document.write( "\"3x%2B2y=6\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"2y=6-3x\" Subtract \"3x\" from both sides.\r
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\n" ); document.write( "\n" ); document.write( "\"2y=-3x%2B6\" Rearrange the terms.\r
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\n" ); document.write( "\n" ); document.write( "\"y=%28-3x%2B6%29%2F%282%29\" Divide both sides by \"2\" to isolate y.\r
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\n" ); document.write( "\n" ); document.write( "\"y=%28%28-3%29%2F%282%29%29x%2B%286%29%2F%282%29\" Break up the fraction.\r
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\n" ); document.write( "\n" ); document.write( "\"y=-%283%2F2%29x%2B3\" Reduce.\r
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\n" ); document.write( "\n" ); document.write( "Looking at \"y=-%283%2F2%29x%2B3\" we can see that the equation is in slope-intercept form \"y=mx%2Bb\" where the slope is \"m=-3%2F2\" and the y-intercept is \"b=3\" \r
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\n" ); document.write( "\n" ); document.write( "Since \"b=3\" this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis\r
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\n" ); document.write( "\n" ); document.write( "So we have one point \r
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\n" ); document.write( "\n" ); document.write( "Now since the slope is comprised of the \"rise\" over the \"run\" this means\r
\n" ); document.write( "\n" ); document.write( "\"slope=rise%2Frun\"\r
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\n" ); document.write( "\n" ); document.write( "Also, because the slope is \"-3%2F2\", this means:\r
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\n" ); document.write( "\n" ); document.write( "\"rise%2Frun=-3%2F2\"\r
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\n" ); document.write( "\n" ); document.write( "which shows us that the rise is -3 and the run is 2. This means that to go from point to point, we can go down 3 and over 2\r
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\n" ); document.write( "\n" ); document.write( "So starting at , go down 3 units \r
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\n" ); document.write( "\n" ); document.write( "and to the right 2 units to get to the next point \r
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\n" ); document.write( "\n" ); document.write( "Now draw a line through these points to graph \"y=-%283%2F2%29x%2B3\"\r
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\n" ); document.write( "\n" ); document.write( " So this is the graph of \"y=-%283%2F2%29x%2B3\" through the points and \r
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\n" ); document.write( "\n" ); document.write( "OR....\r
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\n" ); document.write( "\n" ); document.write( "Method #2\r
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\n" ); document.write( "\n" ); document.write( "To plot \"3x+%2B+2y+=+6\", we can use the x and y intercepts.\r
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x-intercept

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\n" ); document.write( "\n" ); document.write( "To find the x-intercept, plug in \"y=0\" and solve for x\r
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\n" ); document.write( "\n" ); document.write( "\"3x+%2B+2y+=+6\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"3x+%2B+2%280%29+=+6\" Plug in \"y=0\".\r
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\n" ); document.write( "\n" ); document.write( "\"3x+%2B+0+=+6\" Multiply \"2\" and 0 to get 0.\r
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\n" ); document.write( "\n" ); document.write( "\"3x+%2B+0+=+6\" Simplify.\r
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\n" ); document.write( "\n" ); document.write( "\"3x=6\" Multiply.\r
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\n" ); document.write( "\n" ); document.write( "\"x=%286%29%2F%283%29\" Divide both sides by \"3\" to isolate \"x\".\r
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\n" ); document.write( "\n" ); document.write( "\"x=2\" Reduce.\r
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\n" ); document.write( "\n" ); document.write( "So the x-intercept is .\r
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y-intercept

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\n" ); document.write( "\n" ); document.write( "To find the y-intercept, plug in \"x=0\" and solve for y\r
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\n" ); document.write( "\n" ); document.write( "\"3x+%2B+2y+=+6\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"3%280%29+%2B+2y+=+6\" Plug in \"x=0\".\r
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\n" ); document.write( "\n" ); document.write( "\"0+%2B+2y+=+6\" Multiply \"3\" and 0 to get 0.\r
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\n" ); document.write( "\n" ); document.write( "\"+%2B+2y+=+6\" Simplify.\r
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\n" ); document.write( "\n" ); document.write( "\"y=%286%29%2F%282%29\" Divide both sides by \"2\" to isolate \"y\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=3\" Reduce.\r
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\n" ); document.write( "\n" ); document.write( "So the y-intercept is .\r
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\n" ); document.write( "\n" ); document.write( "Now plot the x and y intercepts:\r
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\n" ); document.write( "\n" ); document.write( "Now draw a line through the points to graph the equation \"3x+%2B+2y+=+6\"\r
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\n" ); document.write( "\n" ); document.write( " Graph of \"3x+%2B+2y+=+6\"
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