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

f(x)=−5x−4

f of x is equal to negative 5 x minus 4

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

f(x)=−4x−5

Answer 1

To find the correct equation that describes the function in the table, we should 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 \( x = 3 \), \( y = -17 \)

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

To express the relationship in the form of a linear equation \( y = mx + b \), we find the slope \( m \) first:
- The change in \( y \) (rise) when \( x \) changes by 1 (run):
\[
m = \frac{\Delta y}{\Delta x} = \frac{-4}{1} = -4
\]

Next, we use one of the points (for example, \( (0, -5) \)) to find the y-intercept \( b \):
\[
y = mx + b \implies -5 = -4(0) + b \implies b = -5
\]

Thus, we can express the relationship as:
\[
y = -4x - 5
\]

However, since we want to put this into function notation, we can write:
\[
f(x) = -4x - 5
\]

Therefore, the correct answer from the given options is:
\[
\text{f(x) = −4x − 5}
\]