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, we can observe the relationship between the values of \(x\) and \(y\). The table shows that as \(x\) increases, \(y\) increases by 1 for each increase of 1 in \(x\). This indicates a linear relationship.

We can notice that when \(x = 0\), \(y = -10\). This gives us a starting point. The general form of a linear equation is:

\[ f(x) = mx + b \]

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

1. **Finding the slope (m)**:
The slope \(m\) can be found from the change in \(y\) over the change in \(x\):
\[
m = \frac{\Delta y}{\Delta x} = \frac{-9 - (-10)}{1 - 0} = \frac{1}{1} = 1
\]

2. **Finding the y-intercept (b)**:
From the starting point when \(x = 0\), we see that \(y = -10\), so:
\[
b = -10
\]

Putting it all together, we find:

\[
f(x) = 1x - 10
\]

This can also be simply written as:

\[
f(x) = x - 10
\]

So, in function notation, the answer is:

**f(x) = 1x + (-10)**

or more succinctly:

**f(x) = x - 10**