o show that arithmetic sequence formulas have the same structure as linear functions, choose the linear function equation that has the same structure as the arithmetic sequence an=6+(n−1)⋅8.(1 point)

Question

Responses

y=2x−8
y equals 2 x minus 8

y=8x−2
y equals 8 x minus 2

y=6x+8
y equals 6 x plus 8

y=8x+6
y equals 8 x plus 6

Answer 1

To find the linear function that has the same structure as the arithmetic sequence \( a_n = 6 + (n - 1) \cdot 8 \), we can start by rewriting the arithmetic sequence equation in a more recognizable form.

The equation \( a_n = 6 + (n - 1) \cdot 8 \) can be simplified as follows:

1. Distribute the 8: \[ a_n = 6 + 8n - 8 \]
2. Combine like terms: \[ a_n = 8n - 2 \]

Now, this equation \( a_n = 8n - 2 \) has a structure similar to a linear function \( y = mx + b \) where:

• \( m = 8 \) (the coefficient of \( n \))
• \( b = -2 \) (the constant term)

Thus, the linear function that matches the arithmetic sequence is:

\[ y = 8x - 2 \]

Therefore, the correct response is:

y = 8x - 2.