Use the table to answer the question.

Question

x y
0 −5

1 −9

2 −13

3 −17

Which of the following equations correctly describes the function in the table using function notation?



(1 point)
Responses

f(y)=−4x−5
f left parenthesis y right parenthesis equals negative 4 x minus 5

f(x)=−5x−4

f of x is equal to negative 5 x minus 4

f(y)=−5x−4
f left parenthesis y right parenthesis equals negative 5 x minus 4

f(x)=−4x−5

Answer 1

To find the correct equation that describes the function in the table, we can first identify the pattern in the values of \( y \) as \( x \) increases.

Given the pairs:

• \( (0, -5) \)
• \( (1, -9) \)
• \( (2, -13) \)
• \( (3, -17) \)

We can see that as \( x \) increases by 1, \( y \) decreases by 4. This indicates a linear relationship.

To find the equation in the form \( y = mx + b \):

1. The slope \( m \) is \( -4 \) (the change in \( y \) divided by the change in \( x \)).
2. To find \( b \), we can use one of the points. When \( x = 0 \), \( y = -5 \) implies that \( b = -5 \).

Thus, the equation becomes: \[ y = -4x - 5 \]

In function notation, we express this as: \[ f(x) = -4x - 5 \]

Looking at the responses, the correct choice is: f(x) = -4x - 5.