C. Slope

A linear relation's rate of change corresponds to the slope of the line formed when that relation is graphed. The slope of a line takes into consideration the line's steepness and direction.

Slope
the ratio of the vertical change to the horizontal change of a line or line segment

Δ is the Greek letter delta and is used to represent a change.

Δ y represents the amount of vertical change

Δ x represents the amount of horizontal change.

 The slope of a line measures how steep a line is by comparing the vertical change of the line to the horizontal change of the line. The variable m is often used to represent slope. The following two formulas are equivalent.

 

 Lines with a positive slope increase from left to right.  Lines with a negative slope decrease from left to right.



The rise, or Δy, can be determined by subtracting the y-values of any two points on a line or line segment. This is often written as y 2− y 1. 

The run, or Δx, can be determined by subtracting the x-values of the same two points on the line or line segment. This is often written as x 2− x 1.





When a line is horizontal, the y-values for all points on the line are equal, so the numerator of the slope formula will be 0, which means the slope will be 0.







 When a line is vertical, the x-values for all points on the line are equal, so the denominator of the slope formula will be 0. Division by 0 is undefined, so the slope of a vertical line is said to be undefined.