document.write( "Question 107155This question is from textbook Algebra and Trigonometry Structure And Method
\n" ); document.write( ": Write and equation of the line containing (5,-2) and (8,4)\r
\n" ); document.write( "\n" ); document.write( "a. 2x-y=12
\n" ); document.write( "b.x-2y=9
\n" ); document.write( "c.2x+y=20
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Algebra.Com's Answer #77978 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
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Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (\"5\",\"-2\") and (\"8\",\"4\")
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\n" ); document.write( " \"m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\" Start with the slope formula (note: (\"x%5B1%5D\",\"y%5B1%5D\") is the first point (\"5\",\"-2\") and (\"x%5B2%5D\",\"y%5B2%5D\") is the second point (\"8\",\"4\"))
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\n" ); document.write( " \"m=%284--2%29%2F%288-5%29\" Plug in \"y%5B2%5D=4\",\"y%5B1%5D=-2\",\"x%5B2%5D=8\",\"x%5B1%5D=5\" (these are the coordinates of given points)
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\n" ); document.write( " \"m=+6%2F3\" Subtract the terms in the numerator \"4--2\" to get \"6\". Subtract the terms in the denominator \"8-5\" to get \"3\"
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\n" ); document.write( " \"m=2\" Reduce
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\n" ); document.write( " So the slope is
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\n" ); document.write( " \"m=2\"
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\n" ); document.write( "Now let's use the point-slope formula to find the equation of the line:
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\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 one of the given points
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\n" ); document.write( " So lets use the Point-Slope Formula to find the equation of the line
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\n" ); document.write( " \"y--2=%282%29%28x-5%29\" Plug in \"m=2\", \"x%5B1%5D=5\", and \"y%5B1%5D=-2\" (these values are given)
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\n" ); document.write( " \"y%2B2=%282%29%28x-5%29\" Rewrite \"y--2\" as \"y%2B2\"
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\n" ); document.write( " \"y%2B2=2x%2B%282%29%28-5%29\" Distribute \"2\"
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\n" ); document.write( " \"y%2B2=2x-10\" Multiply \"2\" and \"-5\" to get \"-10%2F1\". Now reduce \"-10%2F1\" to get \"-10\"
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\n" ); document.write( " \"y=2x-10-2\" Subtract \"2\" from both sides to isolate y
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\n" ); document.write( " \"y=2x-12\" Combine like terms \"-10\" and \"-2\" to get \"-12\"
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\n" ); document.write( " Answer:
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\n" ); document.write( " So the equation of the line which goes through the points (\"5\",\"-2\") and (\"8\",\"4\") is:\"y=2x-12\"
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\n" ); document.write( " The equation is now in \"y=mx%2Bb\" form (which is slope-intercept form) where the slope is \"m=2\" and the y-intercept is \"b=-12\"
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\n" ); document.write( " Notice if we graph the equation \"y=2x-12\" and plot the points (\"5\",\"-2\") and (\"8\",\"4\"), we get this: (note: if you need help with graphing, check out this solver)
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\n" ); document.write( " Graph of \"y=2x-12\" through the points (\"5\",\"-2\") and (\"8\",\"4\")
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\n" ); document.write( " Notice how the two points lie on the line. This graphically verifies our answer.
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\n" ); document.write( "\n" ); document.write( "Now lets convert the slope intercept equation into standard form\r
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Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)
Convert from slope-intercept form (y = mx+b) to standard form (Ax+By = C)


\"y+=+2x-12\" Start with the given equation


\"1y-2x+=+2x-12-2x\" Subtract 2x from both sides


\"-2x%2B1y+=+-12\" Simplify


\"-1%2A%28-2x%2B1y%29+=+-1%2A%28-12%29\" Multiply both sides by -1 to make the A coefficient positive (note: this step may be optional; it will depend on your teacher and/or textbook)


\"2x-1y+=+12\" Distribute and simplify


The original equation \"y+=+2x-12\" (slope-intercept form) is equivalent to \"2x-1y+=+12\" (standard form where A > 0)


The equation \"2x-1y+=+12\" is in the form \"Ax%2BBy+=+C\" where \"A+=+2\", \"B+=+-1\" and \"C+=+12\"



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\n" ); document.write( "\n" ); document.write( "\"-1%28-2x%2By%29=-1%2A-12\" Now multiply both sides by -1 to make A positive\r
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\n" ); document.write( "\n" ); document.write( "\"2x-y=12\" Distribute\r
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\n" ); document.write( "\n" ); document.write( "So the equation is \"2x-y=12\" which means the answer is A)
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