document.write( "Question 85093: hi, i am asked to find the standard form of an equationfor a line using the points (9,2) and (5,- 3). can anyone please help me as i am not sure how to do this. thanks \n" ); document.write( "
Algebra.Com's Answer #61308 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 (\"9\",\"2\") and (\"5\",\"-3\")
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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 (\"9\",\"2\") and (\"x%5B2%5D\",\"y%5B2%5D\") is the second point (\"5\",\"-3\"))
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\n" ); document.write( " \"m=%28-3-2%29%2F%285-9%29\" Plug in \"y%5B2%5D=-3\",\"y%5B1%5D=2\",\"x%5B2%5D=5\",\"x%5B1%5D=9\" (these are the coordinates of given points)
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\n" ); document.write( " \"m=+-5%2F-4\" Subtract the terms in the numerator \"-3-2\" to get \"-5\". Subtract the terms in the denominator \"5-9\" to get \"-4\"
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\n" ); document.write( " \"m=5%2F4\" Reduce
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\n" ); document.write( " So the slope is
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\n" ); document.write( " \"m=5%2F4\"
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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=%285%2F4%29%28x-9%29\" Plug in \"m=5%2F4\", \"x%5B1%5D=9\", and \"y%5B1%5D=2\" (these values are given)
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\n" ); document.write( " \"y-2=%285%2F4%29x%2B%285%2F4%29%28-9%29\" Distribute \"5%2F4\"
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\n" ); document.write( " \"y-2=%285%2F4%29x-45%2F4\" Multiply \"5%2F4\" and \"-9\" to get \"-45%2F4\"
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\n" ); document.write( " \"y=%285%2F4%29x-45%2F4%2B2\" Add \"2\" to both sides to isolate y
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\n" ); document.write( " \"y=%285%2F4%29x-37%2F4\" Combine like terms \"-45%2F4\" and \"2\" to get \"-37%2F4\" (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 (\"9\",\"2\") and (\"5\",\"-3\") is:\"y=%285%2F4%29x-37%2F4\"
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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%2F4\" and the y-intercept is \"b=-37%2F4\"
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\n" ); document.write( " Notice if we graph the equation \"y=%285%2F4%29x-37%2F4\" and plot the points (\"9\",\"2\") and (\"5\",\"-3\"), 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%2F4%29x-37%2F4\" through the points (\"9\",\"2\") and (\"5\",\"-3\")
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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( "However, that equation is in slope-intercept form. Lets convert it 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+=+%285%2F4%29x-37%2F4\" Start with the given equation


\"4%2Ay+=+4%2A%28%285%2F4%29x-37%2F4%29\" Multiply both sides by the LCD 4


\"4y+=+5x-37\" Distribute and multiply


\"4y-5x+=+5x-37-5x\" Subtract 5x from both sides


\"-5x%2B4y+=+-37\" Simplify


\"-1%2A%28-5x%2B4y%29+=+-1%2A%28-37%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-4y+=+37\" Distribute and simplify


The original equation \"y+=+%285%2F4%29x-37%2F4\" (slope-intercept form) is equivalent to \"5x-4y+=+37\" (standard form where A > 0)


The equation \"5x-4y+=+37\" is in the form \"Ax%2BBy+=+C\" where \"A+=+5\", \"B+=+-4\" and \"C+=+37\"


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