Mathematics

Problem

Which one of the following pairs of straight lines are perpendicular to each other? a)

x+2y=4

and

2x+y=5

3x+4y=7

and

4x+3y=5

2x+y=1

and

x-2y=3

4x+2y=6

and

2x-y=1

Intuitive explanation

Two lines are perpendicular when the product of their slopes equals $-1$ (or when one is vertical and the other horizontal). The key is to extract or calculate the slope of each line in a pair, then check this perpendicularity condition. Rewrite equations in slope-intercept form if needed, or use the relationship between coefficients in standard form to find slopes quickly.

Intuitive explanation

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