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

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

1 answer

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:

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