document.write( "Question 1195376: A straight line L is perpendicular to the line 2/3 x+5/7 y=1 State the x and y intercepts of the line L \n" ); document.write( "

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document.write( "For the line  Ax + By = C,  the slope is  -A/B  (and y-intercept is C/B).\r
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document.write( "A = 2/3
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document.write( "B = 5/7
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document.write( "C = 1\r
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document.write( "The slope of the given line is thus   -(2/3)/(5/7) = -(2/3)*(7/5) = -14/15\r
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document.write( "The slope of line perpendicular to a given line, is found as follows:
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document.write( "         (slope of perpendicular line)  =  -1/(slope of given line) \r
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document.write( "Thus, if we write the equation of the perpendicular line as y = mx + b,
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document.write( "then   m = -1 / (-14/15) = 15/14.\r
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document.write( "You can then write:   y = (15/14)x + b      (*)\r
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document.write( "Since the problem does not give a point of intersection of the two lines, there is no specific solution.  The x-intercept and y-intercept depend on WHERE the two lines meet.   We can only write the FORM of the y-intercept and x-intercept:\r
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document.write( "     y-intercept (set x=0):  y = b
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document.write( "     x-intercept (set y=0, solve for x):  x = -(14/15)b\r
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document.write( "If you know the point where the lines intersect, then you can solve (*) for b, and then plug that value of b into the bottom two equations to get specific (numerical) intercepts.
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