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?

Answer 1

To determine the equation that describes the function presented in the table, we can first observe how \(y\) changes as \(x\) increases. Let's analyze the values:

\[
\begin{align*}
\text{When } x = 0, & \quad y = -5 \\
\text{When } x = 1, & \quad y = -9 \\
\text{When } x = 2, & \quad y = -13 \\
\text{When } x = 3, & \quad y = -17 \\
\end{align*}
\]

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

Let's express \(y\) in terms of \(x\). The general form of a linear equation is:

\[
y = mx + b
\]

where \(m\) is the slope and \(b\) is the y-intercept. Since \(y\) decreases by 4 for each increase of 1 in \(x\), the slope \(m\) is \(-4\).

To find the y-intercept \(b\), we can use the value of \(y\) when \(x = 0\):

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

Now, we can write the equation for the function:

\[
y = -4x - 5
\]

In function notation, we can express this as:

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

Therefore, the equation that correctly describes the function in the table is:

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