Use the table to answer the question.x y 0−51−92−133−17Which of the following equations correctly describes the function in the table using function notation? (1 point)Responsesf(x)=−5x−4f of x is equal to negative 5 x minus 4f(x)=−4x−5f left parenthesis x right parenthesis equals negative 4 x minus 5f(y)=−5x−4f left parenthesis y right parenthesis equals negative 5 x minus 4f(y)=−4x−5f left parenthesis y right parenthesis equals negative 4 x minus 5

Answer 1

To determine which equation correctly describes the function represented in the table, we need to analyze the provided points:

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

Now, let's calculate the slopes between these points to identify a potential linear relationship:

1. Between \( (0, -5) \) and \( (1, -9) \): \[ \text{slope} = \frac{-9 - (-5)}{1 - 0} = \frac{-9 + 5}{1} = -4 \]

2. Between \( (1, -9) \) and \( (2, -13) \): \[ \text{slope} = \frac{-13 - (-9)}{2 - 1} = \frac{-13 + 9}{1} = -4 \]

3. Between \( (2, -13) \) and \( (3, -17) \): \[ \text{slope} = \frac{-17 - (-13)}{3 - 2} = \frac{-17 + 13}{1} = -4 \]

The slope is consistent at \( -4 \).

Now, using the slope-intercept form \( y = mx + b \):

• We have \( m = -4 \).
• Next, we can use one of the points to find \( b \). Using the point \( (0, -5) \): \[ -5 = -4(0) + b \implies b = -5 \]

So, the equation is: \[ y = -4x - 5 \]

In function notation, this can be written as: \[ f(x) = -4x - 5 \]

Now, looking at the responses given, the correct function is: \[ f(x) = -4x - 5 \]