document.write( "Question 274739: Find the equation of the line through the points (-3,-1) and (-9,-6) \n" ); document.write( "
Algebra.Com's Answer #200469 by jim_thompson5910(35256)\"\" \"About 
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First let's find the slope of the line through the points and \r
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\n" ); document.write( "\n" ); document.write( "Note: is the first point . So this means that \"x%5B1%5D=-3\" and \"y%5B1%5D=-1\".\r
\n" ); document.write( "\n" ); document.write( "Also, is the second point . So this means that \"x%5B2%5D=-9\" and \"y%5B2%5D=-6\".\r
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\n" ); document.write( "\n" ); document.write( "\"m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\" Start with the slope formula.\r
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\n" ); document.write( "\n" ); document.write( "\"m=%28-6--1%29%2F%28-9--3%29\" Plug in \"y%5B2%5D=-6\", \"y%5B1%5D=-1\", \"x%5B2%5D=-9\", and \"x%5B1%5D=-3\"\r
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\n" ); document.write( "\n" ); document.write( "\"m=%28-5%29%2F%28-9--3%29\" Subtract \"-1\" from \"-6\" to get \"-5\"\r
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\n" ); document.write( "\n" ); document.write( "\"m=%28-5%29%2F%28-6%29\" Subtract \"-3\" from \"-9\" to get \"-6\"\r
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\n" ); document.write( "\n" ); document.write( "\"m=5%2F6\" Reduce\r
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\n" ); document.write( "\n" ); document.write( "So the slope of the line that goes through the points and is \"m=5%2F6\"\r
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\n" ); document.write( "\n" ); document.write( "Now remember that the general slope intercept equation is \"y=mx%2Bb\" where 'm' is the slope of the line and 'b' is the y-intercept. We can use this general equation to find the equation of the line.\r
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\n" ); document.write( "\n" ); document.write( "Since the line goes through the point (-3,-1), this means that x=-3 and y=-1. In addition, we know that the slope is \"m=5%2F6\". So we can use these values to solve for 'b'.\r
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\n" ); document.write( "\n" ); document.write( "\"y=mx%2Bb\" Start with the general slope-intercept equation.\r
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\n" ); document.write( "\n" ); document.write( "\"-1=%285%2F6%29%28-3%29%2Bb\" Plug in \"x=-3\", \"y=-1\" and \"m=5%2F6\"\r
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\n" ); document.write( "\n" ); document.write( "\"-1=-15%2F6%2Bb\" Multiply.\r
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\n" ); document.write( "\n" ); document.write( "\"-1=-5%2F2%2Bb\" Reduce.\r
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\n" ); document.write( "\n" ); document.write( "\"-1%2B5%2F2=b\" Add \"5%2F2\" to both sides to isolate 'b'\r
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\n" ); document.write( "\n" ); document.write( "\"3%2F2=b\" Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So the value of 'b' is \"b=3%2F2\"\r
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\n" ); document.write( "\n" ); document.write( "Since \"m=5%2F6\" and \"b=3%2F2\", we can plug these values into \"y=mx%2Bb\" to get \"y=%285%2F6%29x%2B3%2F2\"\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 in slope-intercept form through the points (-3,-1) and (-9,-6) is \"y=%285%2F6%29x%2B3%2F2\"
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