document.write( "Question 199536: Find the equation of a line through the point
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Algebra.Com's Answer #149936 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 \"4\" which goes through the point (\"2\",\"-1\"), 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--1=%284%29%28x-2%29\" Plug in \"m=4\", \"x%5B1%5D=2\", and \"y%5B1%5D=-1\" (these values are given)\r
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\n" ); document.write( "\n" ); document.write( "\"y%2B1=%284%29%28x-2%29\" Rewrite \"y--1\" as \"y%2B1\"\r
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\n" ); document.write( "\n" ); document.write( "\"y%2B1=4x%2B%284%29%28-2%29\" Distribute \"4\"\r
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\n" ); document.write( "\n" ); document.write( "\"y%2B1=4x-8\" Multiply \"4\" and \"-2\" to get \"-8\"\r
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\n" ); document.write( "\n" ); document.write( "\"y=4x-8-1\" Subtract 1 from both sides to isolate y\r
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\n" ); document.write( "\n" ); document.write( "\"y=4x-9\" Combine like terms \"-8\" and \"-1\" to get \"-9\" \r
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\n" ); document.write( "\n" ); document.write( "So the equation of the line with a slope of \"4\" which goes through the point (\"2\",\"-1\") is:\r
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\n" ); document.write( "\n" ); document.write( "\"y=4x-9\" which is now in \"y=mx%2Bb\" form where the slope is \"m=4\" and the y-intercept is \"b=-9\"\r
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\n" ); document.write( "\n" ); document.write( "Notice if we graph the equation \"y=4x-9\" and plot the point (\"2\",\"-1\"), 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=4x-9\" through the point (\"2\",\"-1\")\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 \"4\" and goes through the point (\"2\",\"-1\"), this verifies our answer.
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