For the line  Ax + By = C,  the slope is  -A/B  (and y-intercept is C/B).



A = 2/3

B = 5/7

C = 1



The slope of the given line is thus   -(2/3)/(5/7) = -(2/3)*(7/5) = -14/15





The slope of line perpendicular to a given line, is found as follows:

         (slope of perpendicular line)  =  -1/(slope of given line) 



Thus, if we write the equation of the perpendicular line as y = mx + b,

then   m = -1 / (-14/15) = 15/14.



You can then write:   y = (15/14)x + b      (*)



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:



     y-intercept (set x=0):  y = b

     x-intercept (set y=0, solve for x):  x = -(14/15)b



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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