Question

Create a sequence for y = 2x + 3

Answer 1

To create a sequence from the equation \( y = 2x + 3 \), we can substitute different integer values for \( x \) to get corresponding values for \( y \).

Here's a sequence based on some integer values of \( x \):

1. For \( x = 0 \):
\[
y = 2(0) + 3 = 3
\]

2. For \( x = 1 \):
\[
y = 2(1) + 3 = 5
\]

3. For \( x = 2 \):
\[
y = 2(2) + 3 = 7
\]

4. For \( x = 3 \):
\[
y = 2(3) + 3 = 9
\]

5. For \( x = 4 \):
\[
y = 2(4) + 3 = 11
\]

So, the sequence of \( y \) values corresponding to \( x = 0, 1, 2, 3, 4 \) is:
\[ 3, 5, 7, 9, 11 \]

This sequence can be expressed more generally as:
\[ y_n = 2n + 3 \]
for integers \( n \). Thus, the sequence can be continued indefinitely by substituting larger values for \( n \).