Writing Linear Equations From Tables

Let’s say the following table is given and your job is to find the linear equation.

The first thing that you need to know is that every straight line on a coordinate plane can be written by the following equation. The method is pretty straightforward but we will solve it in a step-by-step method.

y = mx + b 

Here, x is the set of input values, y is the set of output values, m is the slope and b is the y-intercept.

From the table, you can see the values of x and y. Now, you will have to find m and c in order to find the linear equation that satisfies the given values.

Step 1: Finding m

First, we will find m or the slope of the line. To find m, we will use following formula:

m = change in y values/ change in x values ……….. (1)

Now, If we look at the first two rows of the table, we can see that x is changing from 3 to 2 and y is changing from 4 to 1. So, x is changing by -1 and y is changing by -3.

Now using the formula (1), we can get the value of m. So,

m = -3/-1 = 3

Now, we know the value of m. Next, we have to find the value of b.

Step 2: Finding b

To find b, we need to write the straight line equation

y = mx + b 

From the first row of the given table, we can see that when x is 3, y is 4

so, we can write that

m = 3

y = 4

x = 3

Now using the straight line equation, we get

4 = 3(3) + b

4 = 9 + b

From this point, you can solve the equation for b by subtracting 9 from both sides

4 = 9 + b

-9   -9
which will give us b = -5 

So, we have found our m = 3 and b = -5

So, the linear equation will be

y = 3x -5.


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