Write the linear equation that gives the rule for this table. x f(x)
2 27
3 28
4 29
5 30

Write your answer as an equation with f(x) first, followed by an equals sign.

The linear equation that gives the rule of the table is f(x) = x + 25

The linear equation can be represented in a slope intercept form as follows:

y = mx + b

where

m = slope

b = y-intercept

Therefore,

Using the table let get 2 points

(2, 27)(3, 28)

let find the slope

m = 28 - 27 / 3 -2 = 1

let's find b using (2, 27)

27 = 2 + b

b = 25

Therefore,

y = x + 25

f(x) = x + 25

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The linear equation that gives the rule for this table will be:

Step-by-step explanation:

Taking two points from the table

Finding the slope between two points

We know the slope-intercept form of linear equation is

where m is the slope and b is the y-intercept

substituting the point (2, 27) and m=1 in the slope-intercept form to determine the y-intercept 'b'

27 = 1(2)+b

27-2 = b

b = 25

Now, substituting m=1 and b=25 in the slope-intercept form to determine the linear equation

y=mx+b

y=1(x)+25

y=x+25

Thus, the linear equation that gives the rule for this table will be:

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step-by-step explanation: