The equation of the straight line passing through the point \( (1, 1) \) and perpendicular to the line \( x + y = 5 \) is:
Show Hint
- \( x - y = 2 \)
- \( x - y = 0 \)
- \( x - y = -2 \)
- \( x + y = 2 \)
- \( x + y = 0 \)
The Correct Option is B
Solution and Explanation
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 \( x - y = 0 \).
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