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

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
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Answer 1

To find the correct equation that describes the relation between \( x \) and \( y \) in the table, we can analyze the data points:

• When \( x = 0 \), \( y = -5 \)
• When \( x = 1 \), \( y = -9 \)
• When \( x = 2 \), \( y = -13 \)
• When \( x = 3 \), \( y = -17 \)

From the values, we can see that as \( x \) increases by 1, \( y \) decreases by 4. This indicates a linear relationship with a slope of -4.

The general form of a linear equation is given by:

\[ y = mx + b \]

where \( m \) is the slope and \( b \) is the y-intercept.

Let's determine the y-intercept \( b \):

We can use any point from the table. Using the point \( (0, -5) \):

\[ y = -4(0) + b \implies -5 = b \]

So the equation becomes:

\[ y = -4x - 5 \]

Now, we can express this in function notation as:

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

So the correct response from the options given is:

f(x) = -4x - 5