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Can a given point be in more than one line?
Yes. The lines would cross each other
Can one line have 2 slopes?
If the line is a straight line, meaning 180degrees, it can only have one slope. If it is a function (f(x)= or y=) then the line may have more than one, one, or an undefined slope. Find the first differential of the function and plug in your given x value to find the slope at any given point.
True or false Through a point not on a line one ands only one line can be constructed parallel to a given line?
True for the Euclidean plane. There are consistent geometries (for example, projective geometry, or on the surface of a sphere where there may be none or more than one such lines.
Is a horizonal line crosses the graph of a function of f at more than one point?
It can do.
How can you prove that a constructed line is parallel to a given line?
One way is to draw a straight line from the constructed line to the given line. If the lines are parallel, than the acute angle at the given and constructed line will be the same as will be the obtuse angles at the given and constructed line.
