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What do the following two equations represent? - \( 4 x-2 y=-5 \) Choose 1 answer: (A) The same line (B) Distinct parallel lines (C) Perpendicular lines (D) Intersecting, but not perpendicular lines

Ask by Bird Christensen. in the United States
Jan 21,2025

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The two equations represent the **same line**.

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The equation \(4x - 2y = -5\) can be rewritten in slope-intercept form as \(y = 2x + \frac{5}{2}\), which reveals its slope of 2. To determine the relationship with another line, you would analyze the slope of that line. If both lines have the same slope, they are parallel; different slopes mean they will intersect. To check the answer options: if the other line also has a slope of 2, then (B) Distinct parallel lines would be the correct choice. If the slopes are different, then (D) Intersecting, but not perpendicular lines could be true.

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