Recall what is a linear function
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First find m. Look at the table and notice that every time the x terms go up by 1, the y terms go up by 1. This means that m is equal to 1.
Next find b. Take the equation y = mx + b and plug in the m value (m = 1) and a pair of (x, y) coordinates from the table, such as (4, 1). Then solve for b.
y = mx + b
1 = 1(4) + b
1 = 4 + b
-3 = b
Finally, use the m and b values you found (m = 1 and b = -3) to write the equation.
y = mx + b
y = 1x + -3
y = x − 3
So, the linear function is y = f(x) = x -3