The linear equation is f(x) = x + 22 that gives the rule for the given table.
It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.
If in the linear equation one variable is present then the equation is known as the linear equation in one variable.
The data is shown in the table let's suppose the linear equation is represented by the:
f(x) = mx + c
Where m is the slope of the linear equation and c is the y-intercept.
From the table, the difference in x values is 1 ie.
6 - 5 = 7 - 6 = 8 - 7 ⇒ 1
Δx = 1
Similarly the difference in f(x) values is 1 ie.
28 - 27 = 29 - 28 = 30 - 29 ⇒ 1
Δf(x) = 1
The value of m is given by:
[tex]\rm m= \frac{\triangle x}{\triangle f(x)} \Rightarrow \frac{1}{1} \Rightarrow 1[/tex]
For the value of c, put x = 5 and f(x) = 27 in the linear equation, we get:
27 = 1(5) + c
c = 27 - 5⇒ 22
Now the equation is:
f(x) = 1(x) + 22 (m = 1 and c = 22) or
f(x) = x + 22
Thus, the linear equation is f(x) = x + 22 that gives the rule for the given table.
Learn more about the linear equation here:
brainly.com/question/11897796
