Q: What are lines or planes that have tha same slope and do not intersect?

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They are parallel lines which have the same slope but different y intercepts.

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No. The planes must either coincide (they are the same, and intersect everywhere), be parallel (never intersect), or intersect in exactly one line.

They are called skew lines. Explanation: In 3 space, parallel lines must never intersect AND must be in the same plane. If they fail to intersect and are in different planes we call them skew lines.

They are skew lines. Two parallel lines must be in the same plane.

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Lines in the same plane that do not intersect Lines in the same plane that do not intersect Lines in the same plane that do not intersect Lines in the same plane that do not intersect

They are parallel lines which have the same slope but different y intercepts.

They are parallel lines which have the same slope but different y intercepts.

Two lines that are in the same plane and never intersect are called "Parallel," meaning that they are lines with the same slope, but not y-intersect.

triangle

yes two lines intersect to form a point two planes intersect to form a line

Yes, that's what makes them parallel lines - they have the same slope. So they never will intersect with each other. If a set of lines didn't have the same slope, at some point they would intersect and thus would not be parallel.

No. The planes must either coincide (they are the same, and intersect everywhere), be parallel (never intersect), or intersect in exactly one line.

Two parallel lines. Such lines have the same slope.

Skew lines, which live in parallel planes.

They are called skew lines. Explanation: In 3 space, parallel lines must never intersect AND must be in the same plane. If they fail to intersect and are in different planes we call them skew lines.

They are skew lines. Two parallel lines must be in the same plane.