To find the equation that describes the function shown in the table, we can look for a linear relationship between \(X\) and \(Y\). The values given in the table are:
- For \(X = 0\), \(Y = -8\)
- For \(X = 1\), \(Y = -7.5\)
- For \(X = 2\), \(Y = -7\)
- For \(X = 3\), \(Y = -6.5\)
We can see that as \(X\) increases by 1, \(Y\) increases by 0.5. This suggests that the slope \(m\) of the linear function could be \(0.5\):
-
Calculate the slope \(m\): \[ m = \frac{Change , in , Y}{Change , in , X} = \frac{0.5}{1} = 0.5 \]
-
We can use the point-slope form or point-intercept form to determine the linear equation. We know that linear functions can be represented as: \[ Y = mX + b \]
-
Using one of the points, for example, when \(X = 0\), \(Y = -8\), we can find the y-intercept \(b\): \[ -8 = 0.5(0) + b \implies b = -8 \]
So, we have the equation: \[ Y = 0.5X - 8 \]
This corresponds to: \[ f(x) = \frac{1}{2}x - 8 \]
Thus, the correct answer is:
C. f(x) = 1/2x - 8
1 answer