Use the table to answer the question.

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

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

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

f(x)=−5x−4

Answer 1

To find the correct equation that describes the function in the table, we can first look at the values of \( x \) and \( y \):

x    y
0   -5
1   -9
2   -13
3   -17

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

Let's compute the slope \( m \) of the line:

\[ m = \frac{\Delta y}{\Delta x} = \frac{-9 - (-5)}{1 - 0} = \frac{-4}{1} = -4 \]

Now we will use the point-slope form to form the linear equation. The formula for a linear equation is:

\[ y = mx + b \]

Where:

• \( m = -4 \) is the slope
• \( b \) is the y-intercept, which can be found from one of the points in the table.

Using the point \( (0, -5) \): \[ y = -4(0) + b \Rightarrow -5 = b \]

So, the equation becomes:

\[ y = -4x - 5 \]

Using function notation, we write this as:

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

Thus, the correct answer is:

f(x) = -4x - 5