Question

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.

Answer 1

f(x) = 4x - 3

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 =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

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

m =
`(5-1)/(2-1)` = 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