document.write( "Question 186467: A straight line is drawn through the point (3,4). the line cuts the axes at the points A and B such that the area of the triangle OAB is 24. Find the x-intercepts of all such lines \n" ); document.write( "

Algebra.Com's Answer #139784 by josmiceli(19441) $\"\"$ $\"About$

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Call the x-intercept $\"x%5Bi%5D\"$
\n" ); document.write( "Call the y-intercept $\"y%5Bi%5D\"$
\n" ); document.write( "Call the slope $\"m\"$
\n" ); document.write( " $\"%281%2F2%29%2Ax%5Bi%5Dy%5Bi%5D+=+24\"$
\n" ); document.write( " $\"x%5Bi%5Dy%5Bi%5D+=+48\"$
\n" ); document.write( " $\"y%5Bi%5D+=+48%2Fx%5Bi%5D\"$
\n" ); document.write( "and
\n" ); document.write( " $\"m+=+-%28y%5Bi%5D%2Fx%5Bi%5D%29\"$
\n" ); document.write( " $\"m+=+-+%2848%2F%28x%5Bi%5D%29%5E2%29\"$
\n" ); document.write( "The general equation is
\n" ); document.write( " $\"y+=+mx+%2B+b\"$ and goes through (3,4)
\n" ); document.write( "and $\"b\"$ is the y-intercept
\n" ); document.write( " $\"4+=+m%2A3+%2B+b\"$
\n" ); document.write( " $\"4+=+3m+%2B+y%5Bi%5D\"$
\n" ); document.write( " $\"4+=+-3%2A%2848%2F%28x%5Bi%5D%29%5E2%29+%2B+y%5Bi%5D\"$
\n" ); document.write( " $\"4+=+-3%2A%2848%2F%28x%5Bi%5D%29%5E2%29+%2B+48%2Fx%5Bi%5D\"$
\n" ); document.write( " $\"4%2A%28x%5Bi%5D%29%5E2+=+-144+%2B+48x%5Bi%5D\"$
\n" ); document.write( " $\"4%2A%28x%5Bi%5D%29%5E2+-+48x%5Bi%5D+%2B+144+=+0\"$
\n" ); document.write( " $\"%28x%5Bi%5D%29%5E2+-+12x%5Bi%5D+%2B+36+=+0\"$
\n" ); document.write( " $\"%28x%5Bi%5D+-+6%29%5E2+=+0\"$
\n" ); document.write( " $\"x%5Bi%5D+=+6\"$
\n" ); document.write( "The x-intercept is $\"6\"$ answer
\n" ); document.write( "and
\n" ); document.write( " $\"y%5Bi%5D+=+48%2Fx%5Bi%5D\"$
\n" ); document.write( " $\"y%5Bi%5D+=+48%2F6\"$
\n" ); document.write( " $\"y%5Bi%5D+=+8\"$
\n" ); document.write( "check:
\n" ); document.write( " $\"%281%2F2%29%2Ax%5Bi%5Dy%5Bi%5D+=+24\"$
\n" ); document.write( " $\"%281%2F2%29%2A6%2A8+=+24\"$
\n" ); document.write( " $\"24+=+24\"$
\n" ); document.write( " $\"m+=+-%28y%5Bi%5D%2Fx%5Bi%5D%29\"$
\n" ); document.write( " $\"m+=+-%288%2F6%29\"$
\n" ); document.write( " $\"m+=+-%284%2F3%29\"$
\n" ); document.write( "The general equation is:
\n" ); document.write( " $\"y+=+-%284%2F3%29%2Ax+%2B+8\"$
\n" ); document.write( "does it go through (3,4)?
\n" ); document.write( " $\"4+=+-%284%2F3%29%2A3+%2B+8\"$
\n" ); document.write( " $\"4+=+-4+%2B+8\"$
\n" ); document.write( " $\"4+=+4\"$
\n" ); document.write( "OK\r
\n" ); document.write( "
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