To determine the rate of change (slope) and initial value (y-intercept) of a linear function using a table, you typically need to know two points on the line represented in the table.
The rate of change \( m \) can be calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
where \( (x_1, y_1) \) and \( (x_2, y_2) \) are two points from the table.
The initial value of the function is usually the \( y \)-value when \( x = 0 \), which can also be called the y-intercept.
Please provide the data in the table or the specific points so that I can calculate the rate of change and identify the initial value for you.