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.
