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:

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