Determine the initial value and the rate of change of the linear function, as given in the graph round the answer to three decimal places as needed (3,4) (0,3) (3,2) (6,1)
To determine the initial value and the rate of change of the linear function, we can use the formula for the slope-intercept form of a linear equation:
y = mx + b
where m represents the rate of change (slope) and b represents the initial value (y-intercept).
Using the given points:
(3, 4)
(0, 3)
We can find the rate of change (slope) as:
m = (y2 - y1) / (x2 - x1)
m = (3 - 4) / (0 - 3)
m = -1 / -3
m = 1/3
Now, for the initial value:
4 = (1/3) * 3 + b
4 = 1 + b
b = 4 - 1
b = 3
Therefore, the linear function can be expressed as:
y = (1/3)x + 3
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Using the other given points:
(3, 2)
(6, 1)
We can also calculate the rate of change (slope) and initial value:
m = (y2 - y1) / (x2 - x1)
m = (1 - 2) / (6 - 3)
m = -1 / 3
For the initial value:
2 = (-1/3) * 3 + b
2 = -1 + b
b = 3
So, for these points, the linear function can be expressed as:
y = (-1/3)x + 3