A vertical line.
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No, because the gradient of the line becomes infinite. Infinite gradient is equivalent to infinite acceleration at that point. Infinite acceleration (by Newton's Laws) would require infinite force.
The higher the gradient, the more steeper the line will be.
The gradient of a straight line cannot be defined- it's infinity.
The Gradient
An infinite number. Each point on a line, however small the line is, can have a perpendicular through it. And since there are an infinite number of points on any line, the answer is an infinite number.