To determine the y-intercept of the instructor's new rates based on the given points, we need to find the line of best fit or derive the equation from the points provided. The points you provided are:
- (0, 8)
- (2, 27)
- (4, 46)
- (6, 65)
Given that the first point is (0, 8), we already see that when \(x = 0\) (which represents time), the total charge (y) is 8. This point indicates that the y-intercept of the graph is 8.
Therefore, the y-intercept of the instructor's new rates is \(8\) dollars.
If you still want to find the slope and the equation of the line for the other points, you would use the method of least squares or fit a linear function, but it is clear here that the specific y-intercept is already provided by the first data point.
Thus, the final answer is:
The y-intercept is 8 dollars.