Final answer:
To analyze the relationship between variables and complete the table, determine if the growth is linear or non-linear by finding the rule and checking for consistent changes. The slope of the line, representing the rate of change, can be found in a linear equation. A graph represents a function if each x-value corresponds to one y-value.
Step-by-step explanation:
To complete the table with the rule, first determine the relationship between the given values. If the values change by consistent amounts, the rule may be linear, which would also mean the growth is linear. If they change by varying amounts, you might be dealing with a non-linear rule.
The slope of a line represents the rate of change, showing how much the dependent variable changes for each unit increase in the independent variable. If you have an equation of the line in the form y = mx + b, then m is the slope and b is the y-intercept.
In a non-functional table, one independent variable may map to more than one dependent variable, which violates the definition of a function. On a graph, a functional relationship means that for each x-value, there is only one y-value.
To create a graph that represents a function, make sure to plot points such that no two points share the same x-value unless they also share the same y-value.
When analyzing growth, you can calculate and interpret a growth rate by looking at the percentage change in the dependent variable over time. Manipulating a line on a graph involves adjusting its slope or intercept to match the data. Lastly, understanding correlation and calculating the least-squares line help find the best linear fit for a set of data, further enabling us to interpret the relationship between variables.