document.write( "Question 626097: write an equation in standard form for the line described.
\n" ); document.write( "Through (2,9), perpendicular to 5x + y =2
\n" ); document.write( "The equation line is x - ? y = ?.
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Algebra.Com's Answer #393971 by NewtonMathCenter(2)\"\" \"About 
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First of all, if two lines are perpendicular, then their slopes are opposite reciprocals, or in other words, m and -1/m. Thus, to find the slope of the line given, solve for y so it is in the slope-intercept form.
\n" ); document.write( "5x+y=2
\n" ); document.write( "-5x -5x
\n" ); document.write( "y=-5x+2
\n" ); document.write( "The slope-intercept form of the line is y=mx+b where m=slope and b=y-intercept.
\n" ); document.write( "So the slope of this line is -5. The slope of a perpendicular line would then be 1/5.
\n" ); document.write( "For our new line, so far we have the slope, so if we put it into the slope-intercept form, we have y=1/5x+b. If we then substitute (2,9) for (x,y), we will have 9=1/5(2)+b. Now solve for b:
\n" ); document.write( "9=2/5+b
\n" ); document.write( "-2/5 -2/5
\n" ); document.write( "b=9-2/5
\n" ); document.write( "b=45/5-2/5
\n" ); document.write( "b=43/5
\n" ); document.write( "So we have the equation in slope intercept form now: y=1/5x+43/5. To convert this equation to standard form, move the x and eliminate the fractions by multiplying both sides by the lowest common denominator, 5.
\n" ); document.write( "y=1/5x+43/5
\n" ); document.write( "-1/5x -1/5x
\n" ); document.write( "(-1/5x+y=43/5) 5
\n" ); document.write( "-x+5y=43 Standard form should not have a negative coefficient for the x term, so multiply both sides by -1.
\n" ); document.write( "x-5y=-43
\n" ); document.write( "Excellent work:)
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