Question

Use the table to answer the 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(y)=−4x−5
𝑓
(
𝑦
)
=
−
4
𝑥
−
5
f left parenthesis y right parenthesis equals negative 4 x minus 5

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

f(x)=−5x−4
𝑓
(
𝑥
)
=
−
5
𝑥
−
4

f of x is equal to negative 5 x minus 4

f(y)=−5x−4

Answer 1

To determine the correct function based on the given table, we first need to identify the relationship between \(x\) and \(y\).

The values from the table are:

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

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

We can express this relationship in a linear function form: \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

1. **Finding the Slope (m)**:
- The change in \(y\) (which is \(-4\)) over the change in \(x\) (which is \(1\)) gives a slope of:
\[
m = \frac{\Delta y}{\Delta x} = \frac{-4}{1} = -4
\]

2. **Finding the Y-Intercept (b)**:
- When \(x=0\), \(y=-5\). This means the y-intercept \(b\) is \(-5\).

Thus, the equation can be written as:
\[
y = -4x - 5
\]

In function notation, this is typically expressed as:
\[
f(x) = -4x - 5
\]

Now, looking at the options provided, the correct one is:
\[
f(x) = -4x - 5
\]

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