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How can you determine if two straight lines are either parallel or they are perpendicular by merely working on their general equations alone

We can determine if two straight lines are either parallel or they are perpendicular by checking their slopes.

y1 = m1x + b1  (equation for line 1)

y2 = m2x + b2 (equation for line 2)

For two lines to be parallel their slopes have to be same. That is, m1 = m2

If, two straight lines are perpendicular their slopes have to be reciprocal and negative. That is, m1 = -1/m2

Two straight lines are parallel if they have the same slope.

Two straight lines are perpendicular if the product of their slopes is -1.

So, if you know how to find slope, you can get the answer.

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