What does the gradient formula calculate?

The gradient formula specifically calculates the slope of a line between two points on a Cartesian plane. The formula, typically expressed as (y2 - y1) / (x2 - x1), measures the change in the y-coordinates divided by the change in the x-coordinates, effectively determining how steep the line is.

This formula is fundamental in linear equations as it helps in understanding the rate of change; for instance, a higher gradient indicates a steeper line, while a lower gradient suggests a gentler slope. The other options provided relate to different concepts. For example, y = mx + b and y = a + bx are both equations of lines, expressing relationships in slope-intercept form, while y = c + d does not correspond to a standard linear equation's format. By focusing on (y2 - y1) / (x2 - x1), we highlight the essential calculation for the gradient itself.