The algebra shows that the line ax + y + c is perpendicular to the line x - by = d, then a/b = 1.
Firstly, write the equations of line in the slope intercept form. The equation ax + y = can be rewritten as y = ax + c. The slope of the line is m = a.
The equation x - by = d can be written as y = 1/bx - d/b. Therefore, the second slope will be 1/b.
Then, we multiply the slopes. Therefore, (-a)(1/b) = -1.
In conclusion, a/b = 1.
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