Question

what is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point \\((2, 5)\\)?

\\(y + 5 = x + 2\\)
\\(y - 2 = x - 5\\)
\\(y - 5 = -(x - 2)\\)
\\(y + 2 = -(x + 5)\\)

Explanation:

Find the slope of the given line

Using the Slope of a Line knowledge point

$$ m_1 = \frac{2 - (-1)}{4 - 1} = \frac{3}{3} = 1 $$

Determine the perpendicular slope

The slope \(m_2\) of a line perpendicular to a line with slope \(m_1\) satisfies:

$$ m_2 = -\frac{1}{m_1} = -\frac{1}{1} = -1 $$

Write the equation in point-slope form

Using the Point-Slope Form knowledge point

$$
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$$

Answer:

• (A) \(y + 5 = x + 2\)
• (B) \(y - 2 = x - 5\)
• (C) \(y - 5 = -(x - 2)\) (Correct answer)
• (D) \(y + 2 = -(x + 5)\)