Multiple choice general knowledge math & puzzles

The graphs of the two linear equations ax+by=c and bx-ay=c, where a, b and c are all not equal to zero,

  1. are parallel

  2. intersect at one point

  3. intersect at two point

  4. perpendicular
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D Correct answer
Explanation

The slope of ax+by=c is -a/b. The slope of bx-ay=c is b/a. The product of slopes is (-a/b) × (b/a) = -1, which means the lines are perpendicular to each other.

AI explanation

The slope of ax+by=c is -a/b, and the slope of bx-ay=c is b/a. Multiplying these slopes gives (-a/b)×(b/a) = -1, which is the exact condition for two lines to be perpendicular. Since this product is always -1 regardless of the specific nonzero values of a, b, and c, the lines are always perpendicular, not just parallel or intersecting at some arbitrary angle.

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