How do you find the linear model from a table?

You can find a linear model from a table by using a calculator and following these steps:

Steps to Find a Linear Model

Here's how to determine the linear model from a table of data, as described in the provided reference:

Identify x and y Values:
- First, choose one set of values in your table to represent the x-coordinates and the other set to represent the y-coordinates. It is important that the data is represented in corresponding pairs.
Enter Data into Calculator:
- Put your calculator into double stat mode.
- Enter each (x, y) pair as a data point into the calculator.
Calculate Gradient (a) and Y-intercept (b):
- Use your calculator’s functions to find the gradient, often denoted as 'a', and the y-intercept, denoted as 'b'.
Form the Linear Equation:
- The equation will be in the form y = ax + b. Use the calculated values of 'a' and 'b' to write the linear equation representing your data.

Let's imagine you have the following data in a table:

Step 1: You have identified your (x, y) pairs.
Step 2: Enter the data points (1, 3), (2, 5), (3, 7), and (4, 9) into your calculator in double stat mode.
Step 3: Use your calculator to determine that a = 2 and b = 1.
Step 4: Your linear equation is y = 2x + 1.

Linear Model: A representation of a relationship between two variables that can be graphed as a straight line.
Gradient (a): The slope of the line, indicating how much 'y' changes for each unit change in 'x'.
Y-intercept (b): The point where the line crosses the y-axis, representing the value of 'y' when 'x' is zero.

The reference explicitly mentions using a calculator to find the gradient (a) and y-intercept (b). The calculations are typically done by calculators rather than manually.
Make sure your calculator is in "double stat mode" so it can process paired data properly.

By following these steps and using a calculator, you can efficiently determine the linear model that best represents the data provided in your table.