Question

Use the table to answer the question.

x y
0 −10

1 −9

2 −8

3 −7

Using function notation, what is the equation described in the table?

Answer 1

To find the equation that describes the relationship between \( x \) and \( y \) based on the given table, we can observe the pattern in the values:

- When \( x = 0 \), \( y = -10 \)
- When \( x = 1 \), \( y = -9 \)
- When \( x = 2 \), \( y = -8 \)
- When \( x = 3 \), \( y = -7 \)

From the pattern, we can see that as \( x \) increases by 1, \( y \) increases by 1 as well. This indicates a linear relationship.

To express this in function notation, we can write the relationship in the form of \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

1. The slope \( m \) is 1 (since \( y \) increases by 1 for each increase of 1 in \( x \)).
2. Looking at the table, when \( x = 0 \), \( y = -10 \), which is the y-intercept \( b \).

Putting it all together, the equation that describes the relationship in function notation is:

\[
y = 1x - 10
\]

Or simply:

\[
y = x - 10
\]