Final answer:
The relationship between tables, equations, and graphs is integral to understanding the rate of change or slope, where the equation y = mx + b, tables showing the x and y values, and the graphical line slope all represent this linear relationship.
Step-by-step explanation:
The relationship between tables, equations, and graphs in the context of rate of change/slope is foundational in algebra and represents the linear relationship between variables. In mathematics, the equation of a line is typically expressed in the form y = mx + b, where m represents the slope and b represents the y-intercept. The slope indicates how the dependent variable (y) changes relative to changes in the independent variable (x). Tables display values for x and y, allowing us to calculate the change in y over the change in x, which is the slope. Graphs visually depict this relationship; the steeper the line, the greater the rate of change. Changes in the slope or intercept can manipulate the line on a graph and this in turn alters the represented relationship.
Interpreting a straight-line graph involves understanding the slope and y-intercept. The slope describes the rate of change and the y-intercept describes the initial value of the dependent variable when the independent variable is zero. Slope is visually represented on a graph with a line that could be increasing, decreasing, or constant.
For example, in a velocity versus time graph, a line with a constant positive slope indicates a constant velocity increase over time. In cases where acceleration is not constant, as with a car accelerating until a certain speed and then maintaining it, graphs become more complex, showing a changing slope until it reaches a constant value.