Which equation represents the sequence below?

Question

9, 14, 19, 24, 29, . . .

(1 point)
Responses

y=5x+4
y is equal to 5 x plus 4

y=−5x+4
y is equal to negative 5 x plus 4

y=4x−5
y is equal to 4 x minus 5

y=4x+5

Answer 1

To determine the equation that represents the given sequence 9, 14, 19, 24, 29, we first need to identify the pattern and find the formula for the nth term.

1. Identify the pattern:

   • The difference between consecutive terms is 5:
     • 14 - 9 = 5
     • 19 - 14 = 5
     • 24 - 19 = 5
     • 29 - 24 = 5

2. Determine the first term:

   • The first term (when n=1) is 9.

3. Set up the equation:

   • Since the sequence increases by 5 for each subsequent term, it can be expressed as a linear equation.
   • The formula for the nth term of an arithmetic sequence can be given by: \[ y = mx + b \] where \( m \) is the common difference and \( b \) is the first term when \( x=1 \).

4. Calculating the slope (m):

   • The common difference \( m \) = 5.

5. Calculating the y-intercept (b) when \( n=1 \):

   • Let's plug in the first term: \[ y = 5x + b \]
   • For \( x=1 \), we want \( y = 9 \): \[ 9 = 5(1) + b \implies 9 = 5 + b \implies b = 4 \]

6. Create the final equation:

   • Therefore, the equation becomes: \[ y = 5x + 4 \]

Hence, the correct response is: y = 5x + 4.