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)

Answer 1

To express the relationship shown in the table using function notation, we first observe the values of \(y\) for each value of \(x\):

\[
\begin{aligned}
x = 0 & \Rightarrow y = -10 \\
x = 1 & \Rightarrow y = -9 \\
x = 2 & \Rightarrow y = -8 \\
x = 3 & \Rightarrow y = -7 \\
\end{aligned}
\]

From this data, we can see that \(y\) increases by 1 for each increase of 1 in \(x\). This suggests a linear relationship.

We can also find that when \(x = 0\), \(y = -10\), so we have a y-intercept of \(-10\). The slope, which is the change in \(y\) over the change in \(x\), can be calculated as:

\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{-9 - (-10)}{1 - 0} = 1
\]

Using the slope-intercept form of the equation of a line \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept, we can write the equation:

\[
y = 1x - 10
\]

or simply:

\[
y = x - 10
\]

Thus, the equation in function notation is:

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