Question

The equations of the lines which cuts off an intercept \[ - 1\] from y-axis are equally inclined to the axes are
A) \[x - y + 1 = 0,\;{\rm{ }}x + y + 1 = 0\;\;\;\]
B) \[x - y - 1 = 0,\;{\rm{ }}x + y - 1 = 0\]
C) \[x - y - 1 = 0,\;{\rm{ }}x + y + 1 = 0\]
D) None of these

Answer 1

Hint: In this question we have to find the equation of line in which y intercept is given. As y-intercept and indirect slope of line is given in this question therefore a general equation of straight line will be used in this question.

Formula used: In this question a general equation of straight line is used :
\(y = mx + c\)
Where, m is a slope of a line and c is y intercept of a line

Complete step by step solution: Given: y intercept of line is -1 and line is equally inclined to both axes.
\(y = mx + c\)
Line makes equal with both axes therefore angle made line with both axes is or
\(m = \tan \left( \theta \right)\)
\(\theta = 45\;or\;135\)
\(m = \pm 1\)
\(c = - 1\)
\(y = mx + c\)
\(y = \pm 1\left( x \right) - 1\)
\(y = - x - 1\;and\;y = x - 1\)
The equation of straight line is :
\(x + y + 1 = 0\;\;and\;x - y - 1 = 0\)

Thus, Option (C) is correct.

Note: Do not use the equation of line in any other form because it will become very difficult to find the equation of lines and sometimes one may not find the equation of line by using the other equation of lines. In this question it is given that the line makes an equal angle with axes, there are two possibilities of such a line one with angle of and other with angle .