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How to Find the Linear Rule from a Table?

Published in Linear Equations 3 mins read

Finding the linear rule, or the equation of a line, from a table involves determining the slope (m) and the y-intercept (b). The linear rule is typically expressed in the form y = mx + b. The referenced YouTube video titled "How To Write a Linear Equation From a Function Table | Algebra" provides key insights into this process.

Steps to Find the Linear Rule

Here's how to determine the linear rule using information derived from a table of values:

  1. Identify the coordinates: Look at your table and pick out a few pairs of (x,y) values. For example, if your table has:

    x y
    0 -4
    1 -1
    2 2

    We can use (0,-4), (1,-1) and (2,2) as examples.

  2. Calculate the slope (m): The slope is the rate of change of y with respect to x. You can calculate it using any two points (x1, y1) and (x2, y2) from your table:

    • m = (y2 - y1) / (x2 - x1)
    • Using the points (0,-4) and (1,-1), the slope would be:
    • m = (-1 - (-4)) / (1 - 0) = 3 / 1 = 3.
    • If we use (1,-1) and (2,2) to check, m = (2 - (-1)) / (2 - 1) = 3 / 1 = 3.

  3. Determine the y-intercept (b): The y-intercept is the y-value when x is equal to 0.

    • In the table above, when x=0, y=-4; Therefore, b = -4. This aligns with the reference, which states that "the y value is negative four that's our b value that's the y intercept."

  4. Write the linear equation: Using the slope and y-intercept, substitute the values into the equation y = mx + b.

    • In this example, the linear equation is y = 3x - 4.

Example from the reference

The reference identifies a slope (m) and a y-intercept (b), that being -4, that allows us to generate a linear equation.

Practical Insights

  • Consistency Check: Once you have the slope, ensure it's constant by calculating it with different pairs of points from the table. If the slope isn't consistent, the relationship isn't linear.
  • Alternative Method: If (0,b) is not given, you can substitute the slope and any point (x,y) into the y=mx+b equation, and solve for b.
  • Table Structure: The data in the table must be evenly spaced for x for this to work.

Conclusion

By following these steps, you can easily find the linear rule (equation) from a table of values. The key is to calculate the slope and identify the y-intercept.

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