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

f(y)=−5x−4

Answer 1

To determine the correct function from the table provided, let's analyze the relationship between \(x\) and \(y\):

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

We can see that as \(x\) increases by 1, \(y\) decreases by 4. This indicates a linear relationship.

To find the equation of the line, we can use the formula for the slope \(m\):

\[ m = \frac{\Delta y}{\Delta x} = \frac{-4}{1} = -4 \]

Now we can use the point-slope form of a linear equation \(y - y_1 = m(x - x_1)\). Let's use the point \((0, -5)\):

\[ y - (-5) = -4(x - 0) \]

This simplifies to:

\[ y + 5 = -4x \]

\[ y = -4x - 5 \]

Now we can express this in function notation:

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

The equation that correctly describes the function in the table is:

f(x) = -4x - 5

So, the correct response is:

f(x) = -4x - 5