document.write( "Question 507558: If a graph is a line that is perpendicular to the line g(x) = 8x − 4and contains the point (4, 6),determine the linear function \n" ); document.write( "

Algebra.Com's Answer #340538 by oberobic(2304) $\"\"$ $\"About$

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We are given
\n" ); document.write( "g(x) = 8x -4
\n" ); document.write( ".
\n" ); document.write( "By inspection we know
\n" ); document.write( "slope = 8
\n" ); document.write( "y-intercept = -4
\n" ); document.write( "x-intercept = 1/2
\n" ); document.write( ".
\n" ); document.write( "A line perpendicular to this line will have slope = inverse reciprocal:
\n" ); document.write( "slope = -1/8
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\n" ); document.write( "And you want this line to go through the point (4,6).
\n" ); document.write( "OK
\n" ); document.write( ".
\n" ); document.write( "We can define the linear function
\n" ); document.write( ".
\n" ); document.write( "y = -1/8x + b
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\n" ); document.write( "To find 'b' we use the point (4,6)
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\n" ); document.write( "y = mx+b
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\n" ); document.write( "6 = -(1/8)*4 + b
\n" ); document.write( ".
\n" ); document.write( "6 = -1/2 + b
\n" ); document.write( ".
\n" ); document.write( "b = 6 1/2
\n" ); document.write( ".
\n" ); document.write( "y = -(1/8)x + 6 1/2
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\n" ); document.write( " $\"graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C+8%2Ax-4%2C-1%2F8%2Ax%2B6.5%29\"$ \n" ); document.write( "

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