Question
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What do the following two equations represent?

  • Choose 1 answer:
    (A) The same line
    (B) Distinct parallel lines
    © Perpendicular lines
    (D) Intersecting, but not perpendicular lines

Ask by Turner Long. in the United States
Jan 21,2025

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Answer

The two equations represent distinct parallel lines.

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The Deep Dive

These equations represent distinct parallel lines. Both equations have the same slope of , which means they will never intersect, no matter how far they are extended. They are just translated versions of each other, residing on different parts of the Cartesian plane.
To see it more clearly, you can put the second equation in slope-intercept form (y = mx + b). When simplified, it also turns out to have a slope of , affirming that both lines are indeed parallel despite different y-intercepts.

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