How to Determine a Linear Function from a Table: Step-by-Step Guide with Example Table and Equation

linear function from a table

To determine a linear function from a table, follow these steps:

Step 1: Examine the given table and identify two points on the table

To determine a linear function from a table, follow these steps:

Step 1: Examine the given table and identify two points on the table.

For example, suppose we are given the following table:

x | y

1 | 3

4 | 9

We can choose the points (1, 3) and (4, 9) from the table.

Step 2: Calculate the slope (m) of the line passing through the chosen points using the formula:

m = (y2 – y1) / (x2 – x1)

Using our chosen points, we have:

m = (9 – 3) / (4 – 1) = 6 / 3 = 2

So, the slope of the line is 2.

Step 3: Determine the y-intercept (b) of the line, which is the value of y when x equals zero.

To find the y-intercept, substitute one of the points into the slope-intercept form of a linear function: y = mx + b.

Using the point (1, 3):

3 = 2(1) + b

3 = 2 + b

b = 3 – 2

b = 1

Thus, the y-intercept is 1.

Step 4: Write the final equation using the slope-intercept form: y = mx + b.

Using the values we obtained, we have:

y = 2x + 1

Therefore, the linear function that represents the table is y = 2x + 1.

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