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

f(y)=−4x−5

Answer 1

To determine which equation describes the function in the table, we need to observe the relationship between \(x\) and \(y\).

The given points are:
- When \(x = 0\), \(y = -5\)
- When \(x = 1\), \(y = -9\)
- When \(x = 2\), \(y = -13\)
- When \(x = 3\), \(y = -17\)

Now let's analyze the change in \(y\) as \(x\) increases by 1:
- From \(y = -5\) (at \(x = 0\)) to \(y = -9\) (at \(x = 1\)), the change is \( -9 - (-5) = -4\).
- From \(y = -9\) (at \(x = 1\)) to \(y = -13\) (at \(x = 2\)), the change is \( -13 - (-9) = -4\).
- From \(y = -13\) (at \(x = 2\)) to \(y = -17\) (at \(x = 3\)), the change is \( -17 - (-13) = -4\).

This indicates that for each increase of 1 in \(x\), \(y\) decreases by 4. Thus, the slope of the line is \(-4\).

Starting with the slope-intercept form of a linear function \(y = mx + b\), we can see that \(m = -4\).

Now we need to determine the \(y\)-intercept \(b\). Using the point \((0, -5)\):
- When \(x = 0\), \(y = -5\), which gives us \(b = -5\).

Putting this together gives us the equation:
\[
y = -4x - 5
\]

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

From the provided options, the correct equation is:
**f(x) = -4x - 5**