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 function based on the provided table, we need to identify how \(y\) relates to \(x\).

Here is the data from the table:

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

From the data, we can see that as \(x\) increases by 1, \(y\) increases by 1. This suggests that the relationship is linear.

Let's express \(y\) in terms of \(x\) using the slope-intercept form of a linear equation, which is \(y = mx + b\).

1. **Calculating the Slope (m)**:
The change in \(y\) divided by the change in \(x\) gives us the slope:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-9 - (-10)}{1 - 0} = \frac{1}{1} = 1
\]

2. **Finding the y-intercept (b)**:
We can use one of the points to find the y-intercept. Using the point \( (0, -10) \):
\[
b = -10
\]

3. **Writing the Function**:
Now, we can write the function in function notation as follows:
\[
f(x) = 1 \cdot x + (-10)
\]

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

Therefore, the complete answer is:
\[
f(x) = x + (-10)
\]