Exercises 121 and 122: The following data can be modeled by...

Exercises 121 and 122: The following data can be modeled by a linear function. Estimate the value of $x$ when $y=2.99$
$$
\begin{array}{ccccc}
x & 2 & 4 & 6 & 8 \\
\hline y & 0.51 & 1.23 & 1.95 & 2.67
\end{array}
$$

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Key Concepts

Linear Function

A linear function is a mathematical relationship between two variables that can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept. It represents a constant rate of change between the variables, meaning that a change in x by a fixed amount leads to a consistent change in y.

Slope Calculation

The slope is a measure of the steepness or the rate of change of a linear function. It is calculated as the ratio of the change in the dependent variable (y) to the change in the independent variable (x) between any two points on the line. This calculation is crucial for forming the equation of a line from given data points.

Linear Interpolation

Linear interpolation is a method used to estimate an intermediate value within the range of a set of known data points that are assumed to lie on a straight line. By using two adjacent known values and their corresponding x-values, one can calculate the expected value at a specific x, assuming the relationship between the variables is linear.

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