Q: Can a line have two slopes how or why not?

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A straight line cannot have two slopes. A curve, however, might have a different slope at every different point.

Positive 3

a verticla line

For two dimensional lines: Get the formulas for the two lines into a format so that you can evaluate the slope. If the slopes are different, then they will intersect. If the slopes are the same, then you have two parallel lines, or possibly, the two equations describe the same line.

There are two possibilities. If the y intercepts are unique, the lines are parallel. If the y intercepts are the same, the lines are coincident. ( They are the same line)

Related questions

A straight line cannot have two slopes. A curve, however, might have a different slope at every different point.

Yes it can, but it would not then be a straight line but an angle.

If the gable is formed by the two slopes and a horizontal line, it is called a gable roof.

Their slopes are equal.

their slopes are negative reciprocals.

If two lines are parallel, they have the same slope.(And if they are perpendicular, the product of their slopes is minus one - unless one line is horizontal and the other vertical.)

A line that slopes to the right and up has a positive slope.

Positive 3

a verticla line

Given any line L, with slope m, the perpendicular line has slope -m.

For two dimensional lines: Get the formulas for the two lines into a format so that you can evaluate the slope. If the slopes are different, then they will intersect. If the slopes are the same, then you have two parallel lines, or possibly, the two equations describe the same line.

Slopes of line perpendicular to the x-axis are undefined.