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Finding the initial amount and rate of change given a table for a linear function

HELP answer correctly Finding the initial amount and rate of change given a table-example-1
User Alemol
by
7.2k points

1 Answer

5 votes

Answer:

5

=

2

3

(

9

)

+

b

5

=

2

3

9

1

+

b

5

=

2

9

3

1

+

b

5

=

18

3

+

b

5

=

6

+

b

-6

Explanation:

Step 1: Pick two points from the table and plug these points into the rate of change equation. This equation is:

x y

-3 3

3 -1

9 -5

15 -9

21 -13

Δ

Y

Δ

X

=

Y

final

Y

intial

X

final

X

intial

. It is important that we start with the second value when we substitute in the

X

and

Y

values.

Step 2: Simplify the quotient to determine the average rate of change of the table.

Step 3: Replace

m

, in the linear function

y

=

m

x

+

b

, with the average rate of change you calculated in the previous step.

Step 4: Replace

x

and

y

in the

y

=

m

x

+

b

equation with any point from the given table.

Step 5: Simplify the right side of the equal sign.

Step 6: Use inverse operations to solve for

b

. This is the initial amount of the given table.

Rate of Change: This the ratio of the change in

y

to the change in

x

. It can be given by the equation:

Δ

Y

Δ

X

=

Y

final

Y

intial

X

final

X

initial

Initial Amount: This is the

y

value of a table that is produced when

x

is equal to 0.

So, let's try using these steps to find the initial amount and rate of change given a table for a linear function, in the following two examples!

User Georgann
by
7.4k points

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