Question

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

f(x)=−5x−4

f of x is equal to negative 5 x minus 4

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

f(y)=−5x−4
f left parenthesis y right parenthesis equals negative 5 x minus 4
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Answer 1

To find the equation that represents the function described by the table, we can look for a linear relationship between \(x\) and \(y\).

The values from the table are:

\[
\begin{align*}
x & : 0 & y & : -5 \\
1 & : -9 \\
2 & : -13 \\
3 & : -17 \\
\end{align*}
\]

First, we can identify how \(y\) changes as \(x\) increases:

- From \(x = 0\) to \(x = 1\), \(y\) changes from \(-5\) to \(-9\) (a change of \(-4\)).
- From \(x = 1\) to \(x = 2\), \(y\) changes from \(-9\) to \(-13\) (a change of \(-4\)).
- From \(x = 2\) to \(x = 3\), \(y\) changes from \(-13\) to \(-17\) (a change of \(-4\)).

This shows that for every increase of \(x\) by 1, \(y\) decreases by 4. This gives us a slope of \(-4\).

Next, we can use the slope-intercept form of a linear equation, which is

\[
y = mx + b
\]

where \(m\) is the slope and \(b\) is the y-intercept. We can determine \(b\) by substituting one of the points into the equation.

Using the point \( (0, -5) \):

\[
-5 = -4(0) + b \implies b = -5.
\]

So, the equation that describes the relationship between \(x\) and \(y\) is:

\[
y = -4x - 5.
\]

In function notation, this can be written as:

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

Now, looking at the options provided, the correct answer is:

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