Question

The equation of the line passing through the point \( (1, 2) \) and perpendicular to the line \( x + y + 1 = 0 \) is:

• A. \( x + y + 1 = 0 \)
• B. \( x + y - 1 = 0 \)
• C. \( y - x - 1 = 0 \)
• D. \( y - x + 2 = 0 \)
• E. \( y - x - 2 = 0 \)

Hint:

For perpendicular lines, the slope is the negative reciprocal of the given line's slope.

Answer 1

The Correct Option is C

The given equation of the line is: \[ x + y + 1 = 0 \] Rewriting in slope-intercept form: \[ y = -x - 1 \] The slope of this line is \( -1 \). The slope of a line perpendicular to it is the negative reciprocal, which is \( 1 \). 
Using the point-slope formula: \[ y - y_1 = m(x - x_1) \] Substituting \( (x_1, y_1) = (1, 2) \) and \( m = 1 \): \[ y - 2 = 1(x - 1) \Rightarrow y - x = 1 \] Thus, the required equation is: \[ y - x - 1 = 0 \]