Question

The equation of the straight line passing through the point \( (1, 1) \) and perpendicular to the line \( x + y = 5 \) is:

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

Hint:

The equation of a line passing through a point with a given slope is \( y - y_1 = m(x - x_1) \).

Answer 1

The Correct Option is B

Step 1: The slope of the line \( x + y = 5 \) is \( -1 \), since it is in the form \( y = -x + 5 \). 
Step 2: The slope of the line perpendicular to this will be the negative reciprocal of \( -1 \), which is \( 1 \). 
Step 3: Using the point \( (1, 1) \) and the slope \( 1 \), the equation of the line is: \[ y - 1 = 1(x - 1) \quad \Rightarrow \quad y = x \] 
Thus, the equation is \( x - y = 0 \).