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Question
Find the equation of a straight line which cuts an intercept – 2 units from Y-axis and being equally inclined to the axis.
Solution
Since, the required line is equally inclined with coordinate axis, therefore, it makes either an angle of 45° or 135° with the X-axis.
So, its slope is m = tan 45° ⇒ m = 1
or m = tan 135° ⇒ m = -1
Y-intercept, c = -2
Hence, the equation of required lines are
y = mx + x
i.e., y = 1·x - 2 or y = -1·x - 2
⇒ y = x - 2 or y = -x - 2
⇒ x - y - 2 = 0 or x + y + 2 = 0.
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