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.
$$
\begin{array}{|c|c|c|c|}
\hline x & 2 & 4 & 5 \\
\hline f(x) & -1 & -2 & \\
\hline
\end{array}
$$

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Key Concepts

Linear Function

A linear function is a mathematical relationship where the output varies at a constant rate with respect to the input. It is typically expressed in the form f(x) = mx + b, where m represents the slope and b represents the y-intercept. The constant rate of change ensures that the graph of the function is a straight line.

Slope

The slope of a linear function measures the rate at which the dependent variable changes with respect to the independent variable. It is calculated using the formula m = (change in f(x)) / (change in x), which allows for determining how much the output increases or decreases for each unit change in the input.

Table of Values

A table of values for a function organizes selected inputs (x-values) and their respective outputs (f(x) values). For a linear function, this table reflects a consistent change between consecutive entries, meaning that the differences in the function's values should align with the constant slope. This organization helps in identifying patterns and computing missing values.

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