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Question
The equation of the line passing through (1, 2) and perpendicular to x + y + 7 = 0 is ______.
Options
y – x + 1 = 0
y – x – 1 = 0
y – x + 2 = 0
y – x – 2 = 0.
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Solution
The equation of the line passing through (1, 2) and perpendicular to x + y + 7 = 0 is y – x – 1 = 0.
Explanation:
. Let the slope of the line be m.
Then, its equation passing through (1, 2) is given by
y – 2 = m(x – 1) ....(1)
Again, this line is perpendicular to the given line x + y + 7 = 0 whose slope is – 1 (Why?)
Therefore, we have m ( – 1) = – 1
or m = 1
Hence, the required equation of the line is obtained by putting the value of m in (1)
i.e., y – 2 = x – 1
or y – x – 1 = 0
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