document.write( "Question 175495: Write a linear equation in the form y=mx+b givien the following information.
\n" ); document.write( "b) has a slope of 2/3 and passes through the point (12,3).\r
\n" ); document.write( "\n" ); document.write( "c) passes through the points (5,5) (-3,-1) \n" ); document.write( "

Algebra.Com's Answer #130570 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
b)\r
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\n" ); document.write( "\n" ); document.write( "If you want to find the equation of line with a given a slope of $\"2%2F3\"$ which goes through the point ( $\"12\"$ , $\"3\"$ ), you can simply use the point-slope formula to find the equation:\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 the given point\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( " $\"y-3=%282%2F3%29%28x-12%29\"$ Plug in $\"m=2%2F3\"$ , $\"x%5B1%5D=12\"$ , and $\"y%5B1%5D=3\"$ (these values are given)\r
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\n" ); document.write( "\n" ); document.write( " $\"y-3=%282%2F3%29x%2B%282%2F3%29%28-12%29\"$ Distribute $\"2%2F3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y-3=%282%2F3%29x-8\"$ Multiply $\"2%2F3\"$ and $\"-12\"$ to get $\"-8\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=%282%2F3%29x-8%2B3\"$ Add 3 to both sides to isolate y\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%282%2F3%29x-5\"$ Combine like terms $\"-8\"$ and $\"3\"$ to get $\"-5\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So the equation of the line with a slope of $\"2%2F3\"$ which goes through the point ( $\"12\"$ , $\"3\"$ ) is:\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%282%2F3%29x-5\"$ which is now in $\"y=mx%2Bb\"$ form where the slope is $\"m=2%2F3\"$ and the y-intercept is $\"b=-5\"$ \r
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\n" ); document.write( "\n" ); document.write( "Notice if we graph the equation $\"y=%282%2F3%29x-5\"$ and plot the point ( $\"12\"$ , $\"3\"$ ), we get (note: if you need help with graphing, check out this solver )\r
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Graph of $\"y=%282%2F3%29x-5\"$ through the point ( $\"12\"$ , $\"3\"$ )\r
\n" ); document.write( "\n" ); document.write( "and we can see that the point lies on the line. Since we know the equation has a slope of $\"2%2F3\"$ and goes through the point ( $\"12\"$ , $\"3\"$ ), this verifies our answer.\r
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\n" ); document.write( "\n" ); document.write( "c)\r
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\n" ); document.write( "\n" ); document.write( "First let's find the slope of the line through the points

and

and

and

is $\"y=%283%2F4%29x%2B5%2F4\"$ \r
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\n" ); document.write( "\n" ); document.write( " Notice how the graph of $\"y=%283%2F4%29x%2B5%2F4\"$ goes through the points

and

. So this visually verifies our answer.\r
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Graph of $\"y=%283%2F4%29x%2B5%2F4\"$ through the points

and

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