document.write( "Question 174264: 1. find the equation of the line that has a slope of -3/4 and y intercept (0,4).\r
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Algebra.Com's Answer #129198 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
I'll do the first two to get you going in the right direction\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%2F4\" 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=%28-3%2F4%29%28x-0%29\" Plug in \"m=-3%2F4\", \"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=%28-3%2F4%29x%2B%28-3%2F4%29%28-0%29\" Distribute \"-3%2F4\"\r
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\n" ); document.write( "\n" ); document.write( "\"y-4=%28-3%2F4%29x%2B0\" Multiply \"-3%2F4\" and \"-0\" to get \"0\"\r
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\n" ); document.write( "\n" ); document.write( "\"y=%28-3%2F4%29x%2B0%2B4\" Add 4 to both sides to isolate y\r
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\n" ); document.write( "\n" ); document.write( "\"y=%28-3%2F4%29x%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 \"-3%2F4\" which goes through the point (\"0\",\"4\") is:\r
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\n" ); document.write( "\n" ); document.write( "\"y=%28-3%2F4%29x%2B4\" which is now in \"y=mx%2Bb\" form where the slope is \"m=-3%2F4\" 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=%28-3%2F4%29x%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=%28-3%2F4%29x%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 \"-3%2F4\" and goes through the point (\"0\",\"4\"), this verifies our answer.\r
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\n" ); document.write( "\n" ); document.write( "\"y%5E2-11y=-24\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"y%5E2-11y%2B24=0\" Add 24 to both sides.\r
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\n" ); document.write( "\n" ); document.write( "Notice we have a quadratic equation in the form of \"ay%5E2%2Bby%2Bc\" where \"a=1\", \"b=-11\", and \"c=24\"\r
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\n" ); document.write( "\n" ); document.write( "Let's use the quadratic formula to solve for y\r
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\n" ); document.write( "\n" ); document.write( "\"y+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\" Start with the quadratic formula\r
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\n" ); document.write( "\n" ); document.write( "\"y+=+%28-%28-11%29+%2B-+sqrt%28+%28-11%29%5E2-4%281%29%2824%29+%29%29%2F%282%281%29%29\" Plug in \"a=1\", \"b=-11\", and \"c=24\"\r
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\n" ); document.write( "\n" ); document.write( "\"y+=+%2811+%2B-+sqrt%28+%28-11%29%5E2-4%281%29%2824%29+%29%29%2F%282%281%29%29\" Negate \"-11\" to get \"11\". \r
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\n" ); document.write( "\n" ); document.write( "\"y+=+%2811+%2B-+sqrt%28+121-4%281%29%2824%29+%29%29%2F%282%281%29%29\" Square \"-11\" to get \"121\". \r
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\n" ); document.write( "\n" ); document.write( "\"y+=+%2811+%2B-+sqrt%28+121-96+%29%29%2F%282%281%29%29\" Multiply \"4%281%29%2824%29\" to get \"96\"\r
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\n" ); document.write( "\n" ); document.write( "\"y+=+%2811+%2B-+sqrt%28+25+%29%29%2F%282%281%29%29\" Subtract \"96\" from \"121\" to get \"25\"\r
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\n" ); document.write( "\n" ); document.write( "\"y+=+%2811+%2B-+sqrt%28+25+%29%29%2F%282%29\" Multiply \"2\" and \"1\" to get \"2\". \r
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\n" ); document.write( "\n" ); document.write( "\"y+=+%2811+%2B-+5%29%2F%282%29\" Take the square root of \"25\" to get \"5\". \r
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\n" ); document.write( "\n" ); document.write( "\"y+=+%2811+%2B+5%29%2F%282%29\" or \"y+=+%2811+-+5%29%2F%282%29\" Break up the expression. \r
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\n" ); document.write( "\n" ); document.write( "\"y+=+%2816%29%2F%282%29\" or \"y+=++%286%29%2F%282%29\" Combine like terms. \r
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\n" ); document.write( "\n" ); document.write( "\"y+=+8\" or \"y+=+3\" Simplify. \r
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\n" ); document.write( "\n" ); document.write( "So the answers are \"y+=+8\" or \"y+=+3\" \r
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