document.write( "Question 73752This question is from textbook beginning algebra
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\n" ); document.write( "The given ordered pairs are solutions of the same linear equation. Find N.
\n" ); document.write( "(0,1), (4,9), (3,N)
\n" ); document.write( "The book gives the answer as 7. Fine, but how the heck did they get the answer. I can't find anything in the chapter which gives me a hint about how to solve this question. Help !!
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Algebra.Com's Answer #52730 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
Since this is a linear equation (it is a line) the points (0,1), (4,9), (3,N) will all be on the same line. So lets find the equation for the line through the points (0,1), (4,9). First we need the slope
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Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (\"0\",\"1\") and (\"4\",\"9\")
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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 (\"0\",\"1\") and (\"x%5B2%5D\",\"y%5B2%5D\") is the second point (\"4\",\"9\"))
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\n" ); document.write( " \"m=%289-1%29%2F%284-0%29\" Plug in \"y%5B2%5D=9\",\"y%5B1%5D=1\",\"x%5B2%5D=4\",\"x%5B1%5D=0\" (these are the coordinates of given points)
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\n" ); document.write( " \"m=+8%2F4\" Subtract the terms in the numerator \"9-1\" to get \"8\". Subtract the terms in the denominator \"4-0\" to get \"4\"
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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-1=%282%29%28x-0%29\" Plug in \"m=2\", \"x%5B1%5D=0\", and \"y%5B1%5D=1\" (these values are given)
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\n" ); document.write( " \"y-1=2x%2B%282%29%280%29\" Distribute \"2\"
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\n" ); document.write( " \"y-1=2x%2B0\" Multiply \"2\" and \"0\" to get \"0%2F1\". Now reduce \"0%2F1\" to get \"0\"
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\n" ); document.write( " \"y=2x%2B0%2B1\" Add \"1\" to both sides to isolate y
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\n" ); document.write( " \"y=2x%2B1\" Combine like terms \"0\" and \"1\" to get \"1\"
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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 (\"0\",\"1\") and (\"4\",\"9\") is:\"y=2x%2B1\"
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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=1\"
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\n" ); document.write( " Notice if we graph the equation \"y=2x%2B1\" and plot the points (\"0\",\"1\") and (\"4\",\"9\"), 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%2B1\" through the points (\"0\",\"1\") and (\"4\",\"9\")
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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 use the slope and the point (0,1) to find the equation.
\n" ); document.write( "\"y-y%5B1%5D=m%28x-x%5B1%5D%29\"Plug in m=2 and (0,1)
\n" ); document.write( "\"y-1=2%28x-0%29\"
\n" ); document.write( "\"y=2x%2B1\"
\n" ); document.write( "So any more solutions will lie on this line. So to find N, just plug in x=3 to find y
\n" ); document.write( "\"y=2%283%29%2B1\"
\n" ); document.write( "\"y=6%2B1\"
\n" ); document.write( "\"y=7\"
\n" ); document.write( "So the solution is (3,7) which supports the answer. Hope this makes sense. Draw the graph and the points if this is hard to understand.
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