Find the equation of the line that passes through the point (2, 5) and is perpendicular to the line y = 3x + 4.
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Correct answer: D
Explanation
Point = (2, 5)
Line: y = 3x + 4
According to the formula:
The product of the slopes of perpendicular lines = −1
y − y₁ = m(x − x₁)
Slope of the given line = 3
Slope of the perpendicular line:
m × 3 = −1
m = −1/3
Now, substituting the point (2, 5):
y − 5 = −1/3(x − 2)
y − 5 = −x/3 + 2/3
y = −x/3 + 2/3 + 5
y = −x/3 + 17/3