What happens if a line doesn't have a slope?

Answer 1

A line with no slope is a vertical line;

i.e. a line that has a slope of 0, is simply a horizontal line. Mathematically, a line with zero slope corresponds to an equation like y = C, where C is just some constant number like 2, 80, or 1,000,000. If you think about it, since the variable, x, isn't in the above equation, y will equal that constant number, C, for every value of x. So, on a graph, if y is the same number for every position on the x-axis, it's a horizontal line.

A non-mathematical analogue is flat ground. If you're walking on a horizontal surface, like flat ground, you're not going upwards or downwards in elevation, therefore the ground has a zero slope.

The slope of a line is just a number which equals to the tangent of the angle that a line forms with the positive part of the x-axis. Since any vertical line form a 90 degree angle with the x-axis, and tan 90 degrees is undefined, then we say that a vertical line has no slope.