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 correct equation that describes the function represented by the table, we can first analyze the given points:

\[
\begin{align*}
(0, -5) \\
(1, -9) \\
(2, -13) \\
(3, -17) \\
\end{align*}
\]

We can observe that as \( x \) increases, \( y \) decreases.

To find a linear equation of the form \( y = mx + b \), we need to determine the slope \( m \) and the y-intercept \( b \).

1. **Calculate the slope \( m \)**:
Using two points, for example, \( (0, -5) \) and \( (1, -9) \):

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-9 - (-5)}{1 - 0} = \frac{-9 + 5}{1} = \frac{-4}{1} = -4
\]

2. **Find the y-intercept \( b \)**:
We can use the y-value when \( x = 0 \) (which is -5) in the equation \( y = mx + b \):
\[
-5 = -4(0) + b \\
b = -5
\]

Now we have both \( m \) and \( b \). The equation of the function is:

\[
y = -4x - 5
\]

Using function notation, we write:

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

Thus, the correct equation that describes the function in the table is:

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