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

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

f(x)=−5x−4

Answer 1

To find the correct equation that describes the function in the table, we can first look at the values of \( x \) and \( y \):

```
x y
0 -5
1 -9
2 -13
3 -17
```

Next, we notice that as \( x \) increases by 1, \( y \) decreases by 4. This indicates a linear relationship.

Let's compute the slope \( m \) of the line:

\[
m = \frac{\Delta y}{\Delta x} = \frac{-9 - (-5)}{1 - 0} = \frac{-4}{1} = -4
\]

Now we will use the point-slope form to form the linear equation. The formula for a linear equation is:

\[
y = mx + b
\]

Where:
- \( m = -4 \) is the slope
- \( b \) is the y-intercept, which can be found from one of the points in the table.

Using the point \( (0, -5) \):
\[
y = -4(0) + b \Rightarrow -5 = b
\]

So, the equation becomes:

\[
y = -4x - 5
\]

Using function notation, we write this as:

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

Thus, the correct answer is:

**f(x) = -4x - 5**