document.write( "Question 1203209: If the line l^1 : y=kx+b passes the point (2,3) and is perpendicular to the line y = ½x - 5, what is the equation of the line l^1?
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Algebra.Com's Answer #838591 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "The line y = (1/2)x - 5 has slope 1/2
\n" ); document.write( "The negative reciprocal is -2/1 aka -2.
\n" ); document.write( "We flip the fraction and flip the sign to get the perpendicular slope.\r
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\n" ); document.write( "\n" ); document.write( "The mystery line has slope of m = -2
\n" ); document.write( "This line passes through the point (x1,y1) = (2,3)
\n" ); document.write( "Meaning x1 = 2 and y1 = 3.\r
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\n" ); document.write( "\n" ); document.write( "Apply point slope form
\n" ); document.write( "y - y1 = m(x - x1)
\n" ); document.write( "y - 3 = -2(x - 2)
\n" ); document.write( "y - 3 = -2x + 4
\n" ); document.write( "y = -2x + 4 + 3
\n" ); document.write( "y = -2x + 7
\n" ); document.write( "This line has a slope of -2, which is perpendicular to the previous slope 1/2.
\n" ); document.write( "Also, this line goes through (2,3)\r
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\n" ); document.write( "\n" ); document.write( "Check of the 2nd claim
\n" ); document.write( "y = -2x + 7
\n" ); document.write( "3 = -2*2 + 7
\n" ); document.write( "3 = -4 + 7
\n" ); document.write( "3 = 3
\n" ); document.write( "We have confirmed that (2,3) is on the line
\n" ); document.write( "Use of a tool like Desmos or GeoGebra is recommended to visually verify the answer.\r
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\n" ); document.write( "\n" ); document.write( "Answer: y = -2x + 7
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