A graph has time (hours) on the x-axis and total charge (dollars) on the y-axis. Points are at (0, 8), (2, 27), (4, 46), (6, 65).
For the new year, the instructor is thinking of changing his rates. The equation of the possible new rates is represented in the graph. What is the y-intercept of the instructor's new rates?
( ____ , ____ )
The y-intercept of the instructor's new rates is the value of total charge (dollars) when time (hours) is equal to zero.
From the given points, we can see that when time (hours) is equal to 0, the total charge (dollars) is 8.
Therefore, the y-intercept of the instructor's new rates is (0, 8).
To find the y-intercept of the instructor's new rates, we need to determine the value of the y-coordinate when the x-coordinate is 0. The y-intercept occurs when the line intersects the y-axis, which is where x = 0.
Given the points (0, 8), (2, 27), (4, 46), and (6, 65), we can see that the graph is linear, and each point lies on the line.
If we consider the equation of a line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we can determine the y-intercept by finding the value of b.
Let's find the slope first. We can use the formula for the slope of a line, which is:
m = (change in y) / (change in x)
Using the points (0, 8) and (2, 27):
m = (27 - 8) / (2 - 0)
m = 19 / 2
m = 9.5
Now, we can use the equation of a line to find the y-intercept. Plugging in the values for the slope (m) and any point on the line (0, 8):
8 = 9.5(0) + b
8 = b
Therefore, the y-intercept of the instructor's new rates is:
(y-intercept, 8)
So, the answer is (0, 8).