Question

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

Using function notation, what is the equation described in the table?

Answer 1

The given points are:

- \( (0, -10) \)
- \( (1, -9) \)
- \( (2, -8) \)
- \( (3, -7) \)

From these points, we can observe that as \( x \) increases by 1, \( y \) increases by 1 as well. This indicates a linear relationship.

To find the slope (\( m \)) of the line, we can use the formula:

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

Now, using the slope and one of the points, we can use the point-slope form of a linear equation, \( y = mx + b \).

Let's use the point \( (0, -10) \):
- Here, \( x = 0 \) and \( y = -10 \):
\[
-10 = 1(0) + b \implies b = -10
\]

Thus, the equation of the line in function notation is:

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

Therefore, the equation that describes the relationship is:

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