document.write( "Question 100457: WRITE AN EQUATION FOR EACH LINE\r
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Algebra.Com's Answer #73139 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
\"WRITE AN EQUATION FOR EACH LINE\r
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\n" ); document.write( "\n" ); document.write( "When you have a y-intercept of 4, that means the point (0,4) is on the line\r
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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\" which goes through the point (\"0\",\"4\"), 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-4=%282%29%28x-0%29\" Plug in \"m=2\", \"x%5B1%5D=0\", and \"y%5B1%5D=4\" (these values are given)\r
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\n" ); document.write( "\n" ); document.write( "\"y-4=2x%2B%282%29%28-0%29\" Distribute \"2\"\r
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\n" ); document.write( "\n" ); document.write( "\"y-4=2x%2B0\" Multiply \"2\" and \"-0\" to get \"0\"\r
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\n" ); document.write( "\n" ); document.write( "\"y=2x%2B0%2B4\" Add 4 to both sides to isolate y\r
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\n" ); document.write( "\n" ); document.write( "\"y=2x%2B4\" Combine like terms \"0\" and \"4\" to get \"4\" \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\" which goes through the point (\"0\",\"4\") is:\r
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\n" ); document.write( "\n" ); document.write( "\"y=2x%2B4\" which is now in \"y=mx%2Bb\" form where the slope is \"m=2\" and the y-intercept is \"b=4\"\r
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\n" ); document.write( "\n" ); document.write( "Notice if we graph the equation \"y=2x%2B4\" and plot the point (\"0\",\"4\"), 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=2x%2B4\" through the point (\"0\",\"4\")\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\" and goes through the point (\"0\",\"4\"), this verifies our answer.\r
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\n" ); document.write( "\n" ); document.write( "\"WRITE AN EQUATION FOR EACH LINE\r
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\n" ); document.write( "\n" ); document.write( "when you have a slope of 1.5, you really have a slope of \"3%2F2\"\r
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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 \"3%2F2\" which goes through the point (\"0\",\"-4\"), 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--4=%283%2F2%29%28x-0%29\" Plug in \"m=3%2F2\", \"x%5B1%5D=0\", and \"y%5B1%5D=-4\" (these values are given)\r
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\n" ); document.write( "\n" ); document.write( "\"y%2B4=%283%2F2%29%28x-0%29\" Rewrite \"y--4\" as \"y%2B4\"\r
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\n" ); document.write( "\n" ); document.write( "\"y%2B4=%283%2F2%29x%2B%283%2F2%29%28-0%29\" Distribute \"3%2F2\"\r
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\n" ); document.write( "\n" ); document.write( "\"y%2B4=%283%2F2%29x%2B0\" Multiply \"3%2F2\" and \"-0\" to get \"0\"\r
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\n" ); document.write( "\n" ); document.write( "\"y=%283%2F2%29x%2B0-4\" Subtract 4 from both sides to isolate y\r
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\n" ); document.write( "\n" ); document.write( "\"y=%283%2F2%29x-4\" Combine like terms \"0\" and \"-4\" to get \"-4\" \r
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\n" ); document.write( "\n" ); document.write( "So the equation of the line with a slope of \"3%2F2\" which goes through the point (\"0\",\"-4\") is:\r
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\n" ); document.write( "\n" ); document.write( "\"y=%283%2F2%29x-4\" which is now in \"y=mx%2Bb\" form where the slope is \"m=3%2F2\" and the y-intercept is \"b=-4\"\r
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\n" ); document.write( "\n" ); document.write( "Notice if we graph the equation \"y=%283%2F2%29x-4\" and plot the point (\"0\",\"-4\"), 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=%283%2F2%29x-4\" through the point (\"0\",\"-4\")\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 \"3%2F2\" and goes through the point (\"0\",\"-4\"), this verifies our answer.
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