(-1, -4/3)
(-4,-10/3)
Determine the initial value and the rate of change of the linear function as given in the graph
(1 point)
The initial value is 2, and the rate of change is 2/3
The initial value is 2/3 and the rate of change is - 2/3
The initial value is - 2/3 and the rate of change is 2/3
The initial value is 1/6 and the rate of change is 3/7
To determine the initial value and rate of change of the linear function, we need to calculate the slope using the two given points.
The slope is calculated using the formula:
slope = (change in y-values) / (change in x-values)
Using the given points (-1, -4/3) and (-4, -10/3):
change in y-values = -10/3 - (-4/3) = -10/3 + 4/3 = -6/3 = -2
change in x-values = -4 - (-1) = -4 + 1 = -3
slope = (-2) / (-3) = 2/3
Therefore, the rate of change is 2/3.
Now, we can determine the initial value by substituting the slope into the slope-intercept form of a linear equation:
y = mx + b
Using the point (-1, -4/3):
-4/3 = (2/3)(-1) + b
-4/3 = -2/3 + b
-4/3 + 2/3 = b
-2/3 = b
Therefore, the initial value is -2/3.
Thus, the correct answer is: The initial value is -2/3 and the rate of change is 2/3.