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 $y$:

$$\begin{array}{rlr}x& :0123y& :-5-9-13-17\end{array}$$

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 $m$:

$$m=\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}=\frac{-4}{1}=-4$$

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