document.write( "Question 117172: Write an equation in standard form of the line with the given x-intercept and y-intercept.\r
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Algebra.Com's Answer #85213 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
Since the equation has the x-intercept -3 and the y-intercept -5, this means the equation goes through the points (-3,0) and (0,-5)\r
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\n" ); document.write( "\n" ); document.write( "First lets find the slope through the points (\"-3\",\"0\") and (\"0\",\"-5\")\r
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\n" ); document.write( "\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: is the first point (\"-3\",\"0\") and is the second point (\"0\",\"-5\"))\r
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\n" ); document.write( "\n" ); document.write( "\"m=%28-5-0%29%2F%280--3%29\" Plug in \"y%5B2%5D=-5\",\"y%5B1%5D=0\",\"x%5B2%5D=0\",\"x%5B1%5D=-3\" (these are the coordinates of given points)\r
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\n" ); document.write( "\n" ); document.write( "\"m=+-5%2F3\" Subtract the terms in the numerator \"-5-0\" to get \"-5\". Subtract the terms in the denominator \"0--3\" to get \"3\"\r
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\n" ); document.write( "\n" ); document.write( "So the slope is\r
\n" ); document.write( "\n" ); document.write( "\"m=-5%2F3\"\r
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\n" ); document.write( "\n" ); document.write( "Now let's use the point-slope formula to find the equation of the line:\r
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\n" ); document.write( "\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 is one of the given points\r
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\n" ); document.write( "\n" ); document.write( "So lets use the Point-Slope Formula to find the equation of the line\r
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\n" ); document.write( "\n" ); document.write( "\"y-0=%28-5%2F3%29%28x--3%29\" Plug in \"m=-5%2F3\", \"x%5B1%5D=-3\", and \"y%5B1%5D=0\" (these values are given)\r
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\n" ); document.write( "\n" ); document.write( "\"y-0=%28-5%2F3%29%28x%2B3%29\" Rewrite \"x--3\" as \"x%2B3\"\r
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\n" ); document.write( "\n" ); document.write( "\"y-0=%28-5%2F3%29x%2B%28-5%2F3%29%283%29\" Distribute \"-5%2F3\"\r
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\n" ); document.write( "\n" ); document.write( "\"y-0=%28-5%2F3%29x-5\" Multiply \"-5%2F3\" and \"3\" to get \"-15%2F3\". Now reduce \"-15%2F3\" to get \"-5\"\r
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\n" ); document.write( "\n" ); document.write( "\"y=%28-5%2F3%29x-5%2B0\" Add \"0\" to both sides to isolate y\r
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\n" ); document.write( "\n" ); document.write( "\"y=%28-5%2F3%29x-5\" Combine like terms \"-5\" and \"0\" to get \"-5\" \r
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\n" ); document.write( "\n" ); document.write( "So the equation of the line which goes through the points (\"-3\",\"0\") and (\"0\",\"-5\") is:\"y=%28-5%2F3%29x-5\"\r
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\n" ); document.write( "\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=-5\"\r
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\n" ); document.write( "\n" ); document.write( "Notice if we graph the equation \"y=%28-5%2F3%29x-5\" and plot the points (\"-3\",\"0\") and (\"0\",\"-5\"), we get this: (note: if you need help with graphing, check out this solver)\r
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\n" ); document.write( "\n" ); document.write( " Graph of \"y=%28-5%2F3%29x-5\" through the points (\"-3\",\"0\") and (\"0\",\"-5\")\r
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\n" ); document.write( "\n" ); document.write( "Notice how the two points lie on the line. This graphically verifies our answer.\r
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\n" ); document.write( "\n" ); document.write( "Now let's convert the 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+=+%28-5%2F3%29x-5\" Start with the given equation


\"3%2Ay+=+3%2A%28%28-5%2F3%29x-5%29\" Multiply both sides by the LCD 3


\"3y+=+-5x-15\" Distribute and multiply


\"3y%2B5x+=+-5x-15%2B5x\" Add 5x to both sides


\"5x%2B3y+=+-15\" Simplify


The original equation \"y+=+%28-5%2F3%29x-5\" (slope-intercept form) is equivalent to \"5x%2B3y+=+-15\" (standard form where A > 0)


The equation \"5x%2B3y+=+-15\" is in the form \"Ax%2BBy+=+C\" where \"A+=+5\", \"B+=+3\" and \"C+=+-15\"



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\n" ); document.write( "\n" ); document.write( "So the standard equation that x-intercept -3 and the y-intercept -5 is \r
\n" ); document.write( "\n" ); document.write( "\"5x%2B3y=-15\"
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