Proving Equal Differences in Linear Functions over Equal Intervals

The video tutorial explains that linear functions grow by equal differences over equal intervals. It begins by introducing linear functions as equations of the form y = mx + b, with graphs as straight lines. The tutorial demonstrates that for any interval length, the difference in y-coordinates is consistent, depending only on the slope and interval length. A general proof is provided, showing that the difference in heights is independent of specific x-coordinates. An example with a specific line equation further illustrates this concept, confirming that the difference in y-coordinates remains constant for equal intervals.

Describe the relationship between the x-coordinates and the y-coordinates in a linear function.

What conclusion can be drawn about the height differences in linear functions regardless of the x-coordinates?

Provide an example of how to find the difference in y-coordinates for a specific linear function.