document.write( "Question 222940: Find an equation of the line with the given slope and containing the given point.\r
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Algebra.Com's Answer #166854 by jim_thompson5910(35256)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "If you want to find the equation of line with a given a slope of \"2%2F3\" which goes through the point (\"-3\",\"3\"), you can simply use the point-slope formula to find the equation:\r
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\n" ); document.write( "\n" ); document.write( "---Point-Slope Formula---
\n" ); document.write( "\"y-y%5B1%5D=m%28x-x%5B1%5D%29\" where \"m\" is the slope, and is the given point\r
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\n" ); document.write( "\n" ); document.write( "So lets use the Point-Slope Formula to find the equation of the line\r
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\n" ); document.write( "\n" ); document.write( "\"y-3=%282%2F3%29%28x--3%29\" Plug in \"m=2%2F3\", \"x%5B1%5D=-3\", and \"y%5B1%5D=3\" (these values are given)\r
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\n" ); document.write( "\n" ); document.write( "\"y-3=%282%2F3%29%28x%2B3%29\" Rewrite \"x--3\" as \"x%2B3\"\r
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\n" ); document.write( "\n" ); document.write( "\"y-3=%282%2F3%29x%2B%282%2F3%29%283%29\" Distribute \"2%2F3\"\r
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\n" ); document.write( "\n" ); document.write( "\"y-3=%282%2F3%29x%2B2\" Multiply \"2%2F3\" and \"3\" to get \"2\"\r
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\n" ); document.write( "\n" ); document.write( "\"y=%282%2F3%29x%2B2%2B3\" Add 3 to both sides to isolate y\r
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\n" ); document.write( "\n" ); document.write( "\"y=%282%2F3%29x%2B5\" Combine like terms \"2\" and \"3\" to get \"5\" \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So the equation of the line with a slope of \"2%2F3\" which goes through the point (\"-3\",\"3\") is:\r
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\n" ); document.write( "\n" ); document.write( "\"y=%282%2F3%29x%2B5\" which is now in \"y=mx%2Bb\" form where the slope is \"m=2%2F3\" and the y-intercept is \"b=5\"\r
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\n" ); document.write( "\n" ); document.write( "Notice if we graph the equation \"y=%282%2F3%29x%2B5\" and plot the point (\"-3\",\"3\"), we get (note: if you need help with graphing, check out this solver)\r
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\n" ); document.write( "\n" ); document.write( " Graph of \"y=%282%2F3%29x%2B5\" through the point (\"-3\",\"3\")\r
\n" ); document.write( "\n" ); document.write( "and we can see that the point lies on the line. Since we know the equation has a slope of \"2%2F3\" and goes through the point (\"-3\",\"3\"), this verifies our answer.
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