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What is the relationship between the tables, equations and graphs as it relates to rate of change/slope?

User Helbaroudy
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2 Answers

12 votes

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.

User HRKoder
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9 votes

Answer:

What is the relationship between equations and graphs?

Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Step-by-step explanation:

User Golliher
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7.3k points
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