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

f(x)=−5x−4

f of x is equal to negative 5 x minus 4

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

f(x)=−4x−5

Answer 1

To find the correct equation that describes the function in the table, we should analyze the relationship between $x$ and $y$.

From the table:

• When $x=0$, $y=-5$
• When $x=1$, $y=-9$
• When $x=2$, $y=-13$
• When $x=3$, $y=-17$

We can see that as $x$ increases by 1, $y$ decreases by 4. This indicates a linear relationship between $x$ and $y$.

To express the relationship in the form of a linear equation $y=mx+b$, we find the slope $m$ first:

• The change in $y$ (rise) when $x$ changes by 1 (run): $$m=\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}=\frac{-4}{1}=-4$$

Next, we use one of the points (for example, $(0,-5)$) to find the y-intercept $b$: $$y=mx+b⟹-5=-4(0)+b⟹b=-5$$

Thus, we can express the relationship as: $$y=-4x-5$$

However, since we want to put this into function notation, we can write: $$f(x)=-4x-5$$

Therefore, the correct answer from the given options is: $$\text{f(x) = −4x − 5}$$