document.write( "Question 90122This question is from textbook beginning algebra
\n" ); document.write( ": slope 5;y intercept ;(0.4)
\n" ); document.write( "slope 3/4;y intercept (0,8)
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Algebra.Com's Answer #65463 by jim_thompson5910(35256)\"\" \"About 
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\n" ); document.write( "If you want to find the equation of line with a given a slope of \"5\" 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 (\"x%5B1%5D\",\"y%5B1%5D\") 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=%285%29%28x-0%29\" Plug in \"m=5\", \"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=%285%29x-%285%29%280%29%29\" Distribute \"5\"\r
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\n" ); document.write( "\n" ); document.write( "\"y-4=%285%29x%2B%28-5%29%280%29%29\" Multiply the negatives\r
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\n" ); document.write( "\n" ); document.write( "\"y-4=%285%29x%2B0\" Multiply \"-5\" and \"0\" to get \"0\"\r
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\n" ); document.write( "\n" ); document.write( "\"y=%285%29x%2B0%2B4\"Add \"4\" to both sides\r
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\n" ); document.write( "\n" ); document.write( "\"y=5x%2B4\" Combine like terms\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 \"5\" which goes through the point (\"0\",\"4\") is:\r
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\n" ); document.write( "\n" ); document.write( "\"y=5x%2B4\" which is now in \"y=mx%2Bb\" form where the slope is \"m=5\" 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=5x%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=5x%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 \"5\" and goes through the point (\"0\",\"4\"), this verifies our answer.\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\",\"8\"), 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 (\"x%5B1%5D\",\"y%5B1%5D\") 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-8=%283%2F4%29%28x-0%29\" Plug in \"m=3%2F4\", \"x%5B1%5D=0\", and \"y%5B1%5D=8\" (these values are given)\r
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\n" ); document.write( "\n" ); document.write( "\"y-8=%283%2F4%29x-%283%2F4%29%280%29%29\" Distribute \"3%2F4\"\r
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\n" ); document.write( "\n" ); document.write( "\"y-8=%283%2F4%29x%2B%28-3%2F4%29%280%29%29\" Multiply the negatives\r
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\n" ); document.write( "\n" ); document.write( "\"y-8=%283%2F4%29x%2B0\" Multiply \"-3%2F4\" and \"0\" to get \"0\"\r
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\n" ); document.write( "\n" ); document.write( "\"y=%283%2F4%29x%2B0%2B8\"Add \"8\" to both sides\r
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\n" ); document.write( "\n" ); document.write( "\"y=%283%2F4%29x%2B8\" Combine like terms\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\",\"8\") is:\r
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\n" ); document.write( "\n" ); document.write( "\"y=%283%2F4%29x%2B8\" which is now in \"y=mx%2Bb\" form where the slope is \"m=3%2F4\" and the y-intercept is \"b=8\"\r
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\n" ); document.write( "\n" ); document.write( "Notice if we graph the equation \"y=%283%2F4%29x%2B8\" and plot the point (\"0\",\"8\"), 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%2F4%29x%2B8\" through the point (\"0\",\"8\")\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\",\"8\"), this verifies our answer.
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