Question

what is the equation of the line that is parallel to the given line and passes through the point \\((2, 3)\\)?

\\(x + 2y = 4\\)
\\(x + 2y = 8\\)
\\(2x + y = 4\\)
\\(2x + y = 8\\)

Explanation:

Find the slope of the given line

The given line passes through the points \((-4, 0)\) and \((4, -4)\).

$$ m = \frac{-4 - 0}{4 - (-4)} = \frac{-4}{8} = -\frac{1}{2} $$

Determine the equation of the parallel line

A parallel line has the same slope, \(m = -\frac{1}{2}\). Using the point-slope form with the point \((2, 3)\):

$$
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$$

Answer:

• (A) \(x + 2y = 4\)
• (B) \(x + 2y = 8\) (Correct answer)
• (C) \(2x + y = 4\)
• (D) \(2x + y = 8\)