Explain how the “rate of change” and “slope” relates to each other?
The rate of change and slope are related concepts that describe the steepness or incline of a line or a curve.
Slope is the measure of how steep a line is. It is calculated as the ratio of the vertical change (often represented as the difference in y-coordinates) to the horizontal change (often represented as the difference in x-coordinates) between two points on the line. In other words, slope is a measure of how much the y-value changes for every unit change in the x-value.
The rate of change, on the other hand, is a broader concept that can be applied to any situation where there is a change in one variable with respect to another. It represents how much one quantity changes for every unit change in another quantity. For example, in the context of a straight line, the rate of change would be equivalent to the slope.
In summary, both slope and rate of change describe the steepness or incline of a line, with slope specifically referring to straight lines and rate of change being a more general term that can be applied to any situation involving change between two variables.