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

linear function from a table

To understand how to find a linear function from a table, let’s start by discussing what a linear function is

To understand how to find a linear function from a table, let’s start by discussing what a linear function is. A linear function is a mathematical function with a constant rate of change, or in other words, a straight line when graphed.

To determine the linear function from a given table, we need to find the relationship between the inputs (x-values) and outputs (y-values). Let’s take an example table:

x | y
3 | 7
5 | 11
7 | 15
9 | 19
11 | 23

To find the linear function, we need to find the slope and the y-intercept.

1. Finding the slope (m):
The slope represents the rate of change between the x-values and y-values. We can calculate the slope using the formula:

m = (change in y) / (change in x)

For our example table, let’s calculate the slope between the first two points (3,7) and (5,11):

m = (11 – 7) / (5 – 3)
m = 4 / 2
m = 2

So, the slope (m) is 2.

2. Finding the y-intercept (b):
The y-intercept is the value of y when x is equal to 0. To find the y-intercept, we can use any point from the table. Let’s use the first point (3,7). Substitute the values into the equation y = mx + b and solve for b:

7 = 2(3) + b
7 = 6 + b
b = 7 – 6
b = 1

So, the y-intercept (b) is 1.

3. Writing the linear function:
Now that we have the slope (m) and the y-intercept (b), we can write the linear function in the form y = mx + b. Let’s substitute the values into the equation:

y = 2x + 1

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

You can verify this equation by substituting the x-values from the table and checking if the corresponding y-values are obtained.

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