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?(1 point) f(x)= x+

Answer 1

To determine the equation described in the table, let's analyze the given values of \(x\) and \(y\):

| \(x\) | \(y\) |
|-------|-------|
| 0 | -10 |
| 1 | -9 |
| 2 | -8 |
| 3 | -7 |

From the table, we can observe that as \(x\) increases by 1, \(y\) increases by 1 as well. This indicates a linear relationship between \(x\) and \(y\).

Let's express \(y\) in terms of \(x\):
- When \(x = 0\), \(y = -10\)
- When \(x = 1\), \(y = -9\)
- When \(x = 2\), \(y = -8\)
- When \(x = 3\), \(y = -7\)

This suggests a pattern where \(y\) could be represented as a linear function.

To find the equation, we can assume the following linear form:
\[
y = mx + b
\]
where \(m\) is the slope and \(b\) is the y-intercept.

From the table data:
1. The slope \(m\) can be determined as \(1\) because for every increase of \(1\) in \(x\), \(y\) increases by \(1\).
2. The y-intercept \(b\) can be seen when \(x = 0\): \(y = -10\).

Therefore, the equation can be written as:
\[
y = 1x - 10
\]
or simply:
\[
y = x - 10
\]

Using function notation, we can write this as:
\[
f(x) = x - 10
\]

In conclusion, the equation described in the table is:
\[
f(x) = x - 10
\]