The initial amount and rate of change given a table for a linear function are $332 and $22.5, respectively
How to find the initial amount and rate of change given a table for a linear function?
The table of linear function represents the given parameter
On the table, we have the following points
(x, y) = (6, 467) and (10, 647)
The rate of change is calculated as
Rate = (y2 - y1)/(x2 - x1)
So, we have
Rate = (647 - 467)/(10 - 2)
Evaluate
Rate = 22.5
This means that the rate of change is $22.5
The initial amount is calculated as
y = m(x - x1) + y1
Where
m = 22.5
So, we have
y = 22.5(x - x1) + y1
Using one of the points, we have
y = 22.5(x - 6) + 467
Set x = 0
So, we have
y = 22.5(0 - 6) + 467
Evaluate
y = 332
Hence, the initial amount and rate of change given a table for a linear function are $332 and $22.5, respectively
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