Find the initial value and rate of change of these four graph points:

Question

(-3,4)
(0,3)
(3,2)
(6,1)

Answer 1

To find the initial value and rate of change of each graph point, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the rate of change (slope) and b is the initial value (y-intercept).

For point (-3,4):
The initial value (y-intercept) is 4.
To find the rate of change (slope), we can use the formula:
m = (y2 - y1) / (x2 - x1)
m = (3 - 4) / (0 - (-3))
m = -1 / 3

Therefore, the initial value is 4 and the rate of change is -1/3.

For point (0,3):
The initial value (y-intercept) is 3.
To find the rate of change (slope), we can use the formula:
m = (y2 - y1) / (x2 - x1)
m = (2 - 3) / (3 - 0)
m = -1 / 3

Therefore, the initial value is 3 and the rate of change is -1/3.

For point (3,2):
The initial value (y-intercept) is 2.
To find the rate of change (slope), we can use the formula:
m = (y2 - y1) / (x2 - x1)
m = (1 - 2) / (6 - 3)
m = -1 / 3

Therefore, the initial value is 2 and the rate of change is -1/3.

For point (6,1):
The initial value (y-intercept) is 1.
To find the rate of change (slope), we can use the formula:
m = (y2 - y1) / (x2 - x1)
m = (1 - 2) / (6 - 3)
m = -1 / 3

Therefore, the initial value is 1 and the rate of change is -1/3.