Final answer:
The false statement is C. Non-linear relations do not have the same first differences, while linear relations, represented by y = mx + b, do have a constant rate of change (first differences).
Step-by-step explanation:
The student's question asks which of the following statements is false:
- A. The slope of a linear relation also represents the constant of variation.
- B. Slope can be calculated as rise over run.
- C. Non-linear relations have the same first differences.
- D. In the equation y = mx + b, the slope is represented by m.
The false statement among these options is C. Non-linear relations have the same first differences. This is not true since the characteristic of non-linear relations is that their rate of change is not constant, which means that the first differences (the differences in the 'y' values for equal increments of 'x') are not the same.
On the other hand, for linear relations which are represented by the equation y = mx + b, the slope or m represents the constant rate of change, meaning that the first differences are constant. Statement D is correct because m in the equation y = mx + b indeed denotes the slope of the line.
The slope gives us an indication of how steep the line is and indicates the rise over the run (change in y over the change in x).