Question:
A line passes through \( (2, 2) \) and is perpendicular to the line \( 3x + y = 3 \). What is its y-intercept?
A line passes through \( (2, 2) \) and is perpendicular to the line \( 3x + y = 3 \). What is its y-intercept?
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To find the y-intercept of a perpendicular line, first find its slope and use the point-slope form to determine the intercept.
Updated On: Jan 6, 2026
- \( 1/3 \)
- \( 2/3 \)
- 1
- 4/3
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The Correct Option is D
Solution and Explanation
Step 1: Understand the geometry.
The line is perpendicular to \( 3x + y = 3 \), so its slope will be the negative reciprocal of the slope of the given line, which is -1/3.
Step 2: Equation of the perpendicular line.
Using the point-slope form, we find that the y-intercept is \( 4/3 \).
Final Answer: \[ \boxed{4/3} \]
The line is perpendicular to \( 3x + y = 3 \), so its slope will be the negative reciprocal of the slope of the given line, which is -1/3.
Step 2: Equation of the perpendicular line.
Using the point-slope form, we find that the y-intercept is \( 4/3 \).
Final Answer: \[ \boxed{4/3} \]
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