Question

Use the table to answer the question

X= 0 Y= -8
X= 1 Y = -7 1/2
X= 2 Y = -7
X= 3 Y = -6 1/2

Which equation describes the function shown in the table

A. f(y) = 1/2x – 8
B. f(x) = 8x – 1/2
C. f(x) = 1/2x – 8
D. f(y) = 8x – 1/2

Answer 1

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 \(0.5\):

1. Calculate the slope \(m\):
\[
m = \frac{Change \, in \, Y}{Change \, in \, X} = \frac{0.5}{1} = 0.5
\]

2. 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:
\[
Y = mX + b
\]

3. 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**