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 y-intercept.
Steps to Solve
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Identify the Variables First, identify the variables from the table. Let's denote the independent variable as $x$ and the dependent variable as $y$.
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Select Two Points Pick two points from the table to use in the equation. For example, let’s say we select the points $(x_1, y_1)$ and $(x_2, y_2)$.
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Calculate the Slope Use the slope formula to find the slope ($m$) of the line. The formula is: $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$
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Use Point-Slope Form Now, take the slope and one of the points to write the equation in point-slope form: $$ y - y_1 = m(x - x_1) $$
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Convert to Slope-Intercept Form If desired, rearrange the equation into slope-intercept 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 y-intercept.
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.
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