document.write( "Question 87170: The equation of the line through (8,6) and (2,-4) is\r
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\n" ); document.write( "\n" ); document.write( "A. 5x - 3y = 22
\n" ); document.write( "B. Y = 3/5x = 8/5
\n" ); document.write( "C. 3x = 4y = 48
\n" ); document.write( "D. -4x + 2y = -16\r
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Algebra.Com's Answer #63106 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 (\"8\",\"6\") and (\"2\",\"-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 (\"8\",\"6\") and (\"x%5B2%5D\",\"y%5B2%5D\") is the second point (\"2\",\"-4\"))
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\n" ); document.write( " \"m=%28-4-6%29%2F%282-8%29\" Plug in \"y%5B2%5D=-4\",\"y%5B1%5D=6\",\"x%5B2%5D=2\",\"x%5B1%5D=8\" (these are the coordinates of given points)
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\n" ); document.write( " \"m=+-10%2F-6\" Subtract the terms in the numerator \"-4-6\" to get \"-10\". Subtract the terms in the denominator \"2-8\" to get \"-6\"
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\n" ); document.write( " \"m=5%2F3\" Reduce
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\n" ); document.write( " So the slope is
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\n" ); document.write( " \"m=5%2F3\"
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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-6=%285%2F3%29%28x-8%29\" Plug in \"m=5%2F3\", \"x%5B1%5D=8\", and \"y%5B1%5D=6\" (these values are given)
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\n" ); document.write( " \"y-6=%285%2F3%29x%2B%285%2F3%29%28-8%29\" Distribute \"5%2F3\"
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\n" ); document.write( " \"y-6=%285%2F3%29x-40%2F3\" Multiply \"5%2F3\" and \"-8\" to get \"-40%2F3\"
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\n" ); document.write( " \"y=%285%2F3%29x-40%2F3%2B6\" Add \"6\" to both sides to isolate y
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\n" ); document.write( " \"y=%285%2F3%29x-22%2F3\" Combine like terms \"-40%2F3\" and \"6\" to get \"-22%2F3\" (note: if you need help with combining fractions, check out this solver)
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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 (\"8\",\"6\") and (\"2\",\"-4\") is:\"y=%285%2F3%29x-22%2F3\"
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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=5%2F3\" and the y-intercept is \"b=-22%2F3\"
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\n" ); document.write( " Notice if we graph the equation \"y=%285%2F3%29x-22%2F3\" and plot the points (\"8\",\"6\") and (\"2\",\"-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=%285%2F3%29x-22%2F3\" through the points (\"8\",\"6\") and (\"2\",\"-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( "Since none of these answers match the equation in slope-intercept form, lets convert it to 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+=+%285%2F3%29x-22%2F3\" Start with the given equation


\"3%2Ay+=+3%2A%28%285%2F3%29x-22%2F3%29\" Multiply both sides by the LCD 3


\"3y+=+5x-22\" Distribute and multiply


\"3y-5x+=+5x-22-5x\" Subtract 5x from both sides


\"-5x%2B3y+=+-22\" Simplify


\"-1%2A%28-5x%2B3y%29+=+-1%2A%28-22%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)


\"5x-3y+=+22\" Distribute and simplify


The original equation \"y+=+%285%2F3%29x-22%2F3\" (slope-intercept form) is equivalent to \"5x-3y+=+22\" (standard form where A > 0)


The equation \"5x-3y+=+22\" is in the form \"Ax%2BBy+=+C\" where \"A+=+5\", \"B+=+-3\" and \"C+=+22\"



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\n" ); document.write( "\n" ); document.write( "\"-1%28-5x%2B3y%29=-1%2A-22\" Multiply both sides by -1 to make C a positive number\r
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\n" ); document.write( "\n" ); document.write( "\"5x-3y=22\"\r
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\n" ); document.write( "\n" ); document.write( "So the answer is A
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