To determine the rate of change (slope) and the initial value (y-intercept) of the linear function from a table of values, you need two points from the table.
The rate of change (slope \( m \)) between two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
The initial value \( b \) is the value of the function when \( x = 0 \).
Since you did not provide specific points from the table, I can guide you in the right direction if you have a set of numbers or if you identify any two points from the table.
However, looking at the provided options:
- \( m = -7, b = -3 \)
- \( m = -0.5, b = 10.5 \)
- \( m = -3, b = -7 \)
- \( m = -0.5, b = 5.5 \)
You can identify the correct pair by taking potential points from a hypothetical set. If you give me points or values from your table, I can assist you further in calculating anyway you wish.