The values in the table represent a linear function. x 1 2 3 4
f(x) 1 5 9 13

What is the function rule?

Write the rule in function notation, using the slope-intercept form of a line.

Enter your answer in the box.

f(x) = 4x - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m =

with (x₁, y₁ ) = (1, 1) and (x₂, y₂ ) = (2, 5) ← 2 ordered pairs from the table

m = = 4 , thus

y = 4x + c ← is the partial equation

To find c substitute any ordered pair from the table into the partial equation

Using (2, 5) , then

5 = 8 + c ⇒ c = 5 - 8 = - 3

Thus

f(x) = 4x + 3 ← is the function rule

step-by-step explanation: yes