Question

Use the table to answer the 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(x)=−4x−5

f left parenthesis x 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(y)=−4x−5

Answer 1

To determine which equation correctly describes the function in the table, we can observe the pattern in the values of \( y \) based on the values of \( x \).

From the table:
- When \( x = 0, y = -5 \)
- When \( x = 1, y = -9 \)
- When \( x = 2, y = -13 \)
- When \( x = 3, y = -17 \)

Let's take note of how \( y \) changes as \( x \) increases:
- The difference between \( y \) values for consecutive \( x \) values is:
- From \( -5 \) to \( -9 \): change of \( -4 \)
- From \( -9 \) to \( -13 \): change of \( -4 \)
- From \( -13 \) to \( -17 \): change of \( -4 \)

This indicates that the function is linear with a slope of \( -4 \).

Using the slope-intercept form of a linear equation \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept:
- The slope \( m = -4 \)
- To find \( b \), we can use the point when \( x = 0 \) (where \( y \) is \( -5 \)):
- When \( x = 0 \), \( y = b \), thus \( b = -5 \).

So the equation in function notation is:
\[
f(x) = -4x - 5
\]

Therefore, the correct response is:
**f(x) = -4x - 5**.