A table of values for a linear function is given. Fill in...

A table of values for a linear function is given. Fill in the missing value and calculate $m$ in each case.
$$
\begin{array}{|c|c|c|c|}
\hline x & -1 & 0 & 1 \\
\hline y & -1 & -3 & \\
\hline
\end{array}
$$

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Key Concepts

Constant Rate of Change

Because linear functions have a constant rate of change, any two pairs of values from the function yield the same slope. This principle can be applied to find any missing value in a table of values by ensuring consistent differences between outputs for equal differences in inputs.

Table of Values

A table of values is used to display corresponding input-output pairs for a function. In the context of linear functions, it helps to illustrate the constant rate of change, making it possible to verify the linearity and compute missing values.

Slope

The slope of a linear function is the measure of its steepness, calculated as the ratio of the change in the output value to the change in the input value. It indicates how much the function's value increases or decreases as the input increases by one unit.

Linear Function

A linear function describes a relationship where the change in the dependent variable is constant with respect to the independent variable. This results in a straight line when graphed, characterized by a constant rate of change.

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