document.write( "Question 944143: Find the slopes of the line containing each pair of points.
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Algebra.Com's Answer #582827 by EdenWolf(517)\"\" \"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 (\"-2\",\"3\") and (\"4\",\"5\")
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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 (\"-2\",\"3\") and (\"x%5B2%5D\",\"y%5B2%5D\") is the second point (\"4\",\"5\"))
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\n" ); document.write( " \"m=%285-3%29%2F%284--2%29\" Plug in \"y%5B2%5D=5\",\"y%5B1%5D=3\",\"x%5B2%5D=4\",\"x%5B1%5D=-2\" (these are the coordinates of given points)
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\n" ); document.write( " \"m=+2%2F6\" Subtract the terms in the numerator \"5-3\" to get \"2\". Subtract the terms in the denominator \"4--2\" to get \"6\"
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\n" ); document.write( " \"m=1%2F3\" Reduce
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\n" ); document.write( " So the slope is
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\n" ); document.write( " \"m=1%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-3=%281%2F3%29%28x--2%29\" Plug in \"m=1%2F3\", \"x%5B1%5D=-2\", and \"y%5B1%5D=3\" (these values are given)
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\n" ); document.write( " \"y-3=%281%2F3%29%28x%2B2%29\" Rewrite \"x--2\" as \"x%2B2\"
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\n" ); document.write( " \"y-3=%281%2F3%29x%2B%281%2F3%29%282%29\" Distribute \"1%2F3\"
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\n" ); document.write( " \"y-3=%281%2F3%29x%2B2%2F3\" Multiply \"1%2F3\" and \"2\" to get \"2%2F3\"
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\n" ); document.write( " \"y=%281%2F3%29x%2B2%2F3%2B3\" Add \"3\" to both sides to isolate y
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\n" ); document.write( " \"y=%281%2F3%29x%2B11%2F3\" Combine like terms \"2%2F3\" and \"3\" to get \"11%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 (\"-2\",\"3\") and (\"4\",\"5\") is:\"y=%281%2F3%29x%2B11%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=1%2F3\" and the y-intercept is \"b=11%2F3\"
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\n" ); document.write( " Notice if we graph the equation \"y=%281%2F3%29x%2B11%2F3\" and plot the points (\"-2\",\"3\") and (\"4\",\"5\"), we get this: (note: if you need help with graphing, check out this solver)
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\n" ); document.write( " Graph of \"y=%281%2F3%29x%2B11%2F3\" through the points (\"-2\",\"3\") and (\"4\",\"5\")
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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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Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (\"-7\",\"2\") and (\"-7\",\"6\")
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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 (\"-7\",\"2\") and (\"x%5B2%5D\",\"y%5B2%5D\") is the second point (\"-7\",\"6\"))
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\n" ); document.write( " \"m=%286-2%29%2F%28-7--7%29\" Plug in \"y%5B2%5D=6\",\"y%5B1%5D=2\",\"x%5B2%5D=-7\",\"x%5B1%5D=-7\" (these are the coordinates of given points)
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\n" ); document.write( " \"m=+4%2F0\" Subtract the terms in the numerator \"6-2\" to get \"4\". Subtract the terms in the denominator \"-7--7\" to get \"0\"
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\n" ); document.write( " Since the denominator is zero, the slope is undefined (remember you cannot divide by zero). So we cannot use the slope intercept form to write an equation. So we can only say that the equation is a vertical line through \"x=-7\", which means the equation is \"x=-7\" (notice this is not in slope-intercept form)
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\n" ); document.write( " So the equation \"x=-7\" looks like this:
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\n" ); document.write( " Graph of \"x=-7\" through the points (\"-7\",\"2\") and (\"-7\",\"6\")
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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 (\"3\",\"2\")
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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 (\"3\",\"2\"))
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\n" ); document.write( " \"m=%282-2%29%2F%283-5%29\" Plug in \"y%5B2%5D=2\",\"y%5B1%5D=2\",\"x%5B2%5D=3\",\"x%5B1%5D=5\" (these are the coordinates of given points)
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\n" ); document.write( " \"m=+0%2F-2\" Subtract the terms in the numerator \"2-2\" to get \"0\". Subtract the terms in the denominator \"3-5\" to get \"-2\"
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\n" ); document.write( " \"m=0\" Reduce
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\n" ); document.write( " So the slope is
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\n" ); document.write( " \"m=0\"
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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=%280%29%28x-5%29\" Plug in \"m=0\", \"x%5B1%5D=5\", and \"y%5B1%5D=2\" (these values are given)
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\n" ); document.write( " \"y-2=0x%2B%280%29%28-5%29\" Distribute \"0\"
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\n" ); document.write( " \"y-2=0x%2B0\" Multiply \"0\" and \"-5\" to get \"0%2F0\". Now reduce \"0%2F0\" to get \"0\"
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\n" ); document.write( " \"y=0x%2B0%2B2\" Add \"2\" to both sides to isolate y
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\n" ); document.write( " \"y=0x%2B2\" Combine like terms \"0\" and \"2\" to get \"2\"
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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 (\"3\",\"2\") is:\"y=0x%2B2\"
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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=0\" and the y-intercept is \"b=2\"
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\n" ); document.write( " Notice if we graph the equation \"y=0x%2B2\" and plot the points (\"5\",\"2\") and (\"3\",\"2\"), we get this: (note: if you need help with graphing, check out this solver)
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\n" ); document.write( " Graph of \"y=0x%2B2\" through the points (\"5\",\"2\") and (\"3\",\"2\")
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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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