Question

the given line passes through the points \\((-4, -3)\\) and \\((4, 1)\\).

what is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point \\((-4, 3)\\)?

\\(y - 3 = -2(x + 4)\\)
\\(y - 3 = -\frac{1}{2}(x + 4)\\)
\\(y - 3 = \frac{1}{2}(x + 4)\\)
\\(y - 3 = 2(x + 4)\\)

Explanation:

Calculate the slope of the given line

Using the Slope of a Line knowledge point

$$ m_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - (-3)}{4 - (-4)} = \frac{4}{8} = \frac{1}{2} $$

Find the perpendicular slope

Using the Perpendicular Line Equations knowledge point

$$ m_2 = -\frac{1}{m_1} = -\frac{1}{1/2} = -2 $$

Write the equation in point-slope form

Using the Point-Slope Form knowledge point

$$
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$$

Answer:

• (A) \(y-3=-2(x+4)\) (Correct answer)
• (B) \(y-3=-\frac{1}{2}(x+4)\)
• (C) \(y-3=\frac{1}{2}(x+4)\)
• (D) \(y-3=2(x+4)\)