Question

use the image to answer the question.
write the function of the graphed arithmetic sequence.
(2 points)
the function of the arithmetic sequence is \\(\square\\).

Explanation:

Step1: Recall arithmetic sequence formula

The formula for an arithmetic sequence (linear function) is \( f(x)=a_1+(x - 1)d\), but also can be written in slope - intercept form \( y=mx + b\) where \( m\) is the common difference (slope) and \( b\) is the initial term (\(a_0\)).

Step2: Find the slope (\(m\))

Using two points \((x_1,y_1)=(0,13)\) and \((x_2,y_2)=(1,20)\), the slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{20 - 13}{1 - 0}=7\).

Step3: Identify the y - intercept (\(b\))

From the point \((0,13)\), when \(x = 0\), \(y=b = 13\).

Step4: Write the function

Using the slope - intercept form \(y=mx + b\), substitute \(m = 7\) and \(b = 13\). So the function is \(f(x)=7x + 13\) (or \(y = 7x+13\)).

Answer:

\(f(x)=7x + 13\) (or \(y = 7x + 13\))