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Yes, but only if they are exactly vertical and exactly horizontal (90 degrees angular difference). For real-world examples, many vertical lines can be perpendicular to a single "horizontal" curved line at the points of intersection.
A line whose slope is not constant or not defined. A curved line, a discontinuous line, a vertical line are some examples.
Yes, technically a curved line can be a line segment, a line in general is something that can be curved or straight
If the graph is a non-vertical straight line, then the rate of change is constant. If the line is curved, then the rate of change (slope) varies.
A vertical line!