Can two lines that intersect be parallel to each other?
What does "parallel" even mean?
No. Parallel lines never intersect.
Can two lines that lie on the same plane be parallel to each other?
To be clear, the question is if they can be parallel, not if they must be parallel.
Yes, two lines that lie on the same plane may be parallel, but they don't have to be.
Line u is parallel to line l and line l is parallel to line i. Is it true that line u is parallel to line i?
Assume that u, l, and i are three different lines. What are their slopes?
Yes, u is parallel to i. Actually, u is parallel to me.
Line j is parallel to line k. If line j has the equation y = 3x – 1, what slope must line k have?
Two lines that are parallel must have the same slope.
Line k must have a slope of 3.
Line p is parallel to line q. If line p has the equation 4x + 5y = 15 and line q passes through point (5, 5), what is the equation of line q?
If we find the slope of line p, we'll have the slope of line q.
The equation of line q is y = -⅘x + 9.
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