How to find a linear equation from a table?
Understand the Problem
The question is asking for a method to derive a linear equation based on given values from a table. This typically involves identifying patterns in the data to establish a relationship between variables.
Answer
The linear equation will be in the form $y = mx + b$.
Answer for screen readers
The linear equation derived from the values will depend on the specific points selected. The general form will be (y = mx + b), where $m$ and $b$ are obtained from the calculated slope and the yintercept.
Steps to Solve

Identify the Variables First, identify the variables from the table. Let's denote the independent variable as $x$ and the dependent variable as $y$.

Select Two Points Pick two points from the table to use in the equation. For example, letâ€™s say we select the points $(x_1, y_1)$ and $(x_2, y_2)$.

Calculate the Slope Use the slope formula to find the slope ($m$) of the line. The formula is: $$ m = \frac{y_2  y_1}{x_2  x_1} $$

Use PointSlope Form Now, take the slope and one of the points to write the equation in pointslope form: $$ y  y_1 = m(x  x_1) $$

Convert to SlopeIntercept Form If desired, rearrange the equation into slopeintercept form ($y = mx + b$) by solving for $y$.
The linear equation derived from the values will depend on the specific points selected. The general form will be (y = mx + b), where $m$ and $b$ are obtained from the calculated slope and the yintercept.
More Information
Linear equations are a fundamental component of algebra and are useful for understanding relationships between variables. Once you have the slope and a point, you can easily express the line that fits the data.
Tips
 Choosing Incorrect Points: Make sure to choose points that are clearly on the line represented by the data in the table.
 Calculating Slope Incorrectly: Ensure the correct subtraction order in the slope formula.
 Failing to Simplify: After finding the equation, always check whether it can be simplified further.