Use the table to answer the question.

Question

x y
0 −5
−
5
1 −9
−
9
2 −13
−
13
3 −17
−
17
Which of the following equations correctly describes the function in the table using function notation?



(1 point)
Responses

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

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

f(x)=−5x−4
𝑓
(
𝑥
)
=
−
5
𝑥
−
4

f of x is equal to negative 5 x minus 4

f(y)=−4x−5

Answer 1

To determine the correct function that describes the data in the table, we first analyze the relationship between \( x \) and \( y \):

From the table:

• When \( x = 0 \), \( y = -5 \)
• When \( x = 1 \), \( y = -9 \)
• When \( x = 2 \), \( y = -13 \)
• When \( x = 3 \), \( y = -17 \)

Next, we observe how \( y \) changes as \( x \) increases. We see that for each increase of 1 in \( x \), \( y \) decreases by 4. Therefore, the slope \( m \) of the function is -4.

Now, we find the y-intercept (when \( x = 0 \)), which is -5.

Therefore, the linear equation that relates \( y \) with \( x \) in the slope-intercept form \( y = mx + b \) becomes:

\[ y = -4x - 5 \]

In function notation, we write this as:

\[ f(x) = -4x - 5 \]

Now, looking at the provided responses, the correct one is:

f(x) = -4x - 5