A slope of 0 is a horizontal line; a vertical line (x₁ = x₂) has an undefined slope, since division by zero is not possible.
Distance is just the Pythagorean theorem applied to the horizontal and vertical gaps between the two points.
The line equation is given in slope-intercept form, y = mx + b, where b is found by substituting one point back in.
What does a negative slope mean?
The line falls from left to right — as x increases, y decreases. A positive slope rises left to right; a slope of zero is flat.
Why is the slope "undefined" for some points?
When both points share the same x-coordinate, the line between them is vertical, and slope (change in y over change in x) would require dividing by zero — mathematically undefined, not zero.
How is the midpoint useful?
It is the exact centre point of the line segment joining the two points — the average of their x-coordinates and the average of their y-coordinates.