Use the table to answer the question.

Question

Use the table to answer the 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)=−4x−5
f left parenthesis x right parenthesis equals negative 4 x minus 5

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

Answer 1

Bot GPT 4-o mini answered
2 hours ago

To find the correct equation that describes the function represented in the table, we first analyze the provided points (x, y):

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

Next, we need to determine the relationship between \( x \) and \( y \). To do this, we can observe how \( y \) changes as \( x \) increases:

From \( x = 0 \) to \( x = 1 \), \( y \) changes from \(-5\) to \(-9\), a change of \(-4\).
From \( x = 1 \) to \( x = 2 \), \( y \) changes from \(-9\) to \(-13\), again a change of \(-4\).
From \( x = 2 \) to \( x = 3 \), \( y \) changes from \(-13\) to \(-17\), once more a change of \(-4\).

This consistent rate of change indicates that the function has a slope of \(-4\).

Using the slope-intercept form of a linear equation, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we start with \( m = -4 \). We can find \( b \) by substituting one of the points into the equation.

Using the point (0, -5):

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

So the equation that describes the data is:

\[ y = -4x - 5 \]

Now, writing it in function notation:

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

From the options provided, the correct equation is:

f(x) = -4x - 5.