Question

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Tony opens a savings account. The graph represents the amount of money in dollars that Tony expects to deposit in his account in terms of the number of years since opening the account.

Answer 1

We have been given that a graph that represents the amount of money in dollars that Tony expects to deposit in his account in terms of the number of years since opening the account.

We are asked to find the rate of change and initial value from our given graph.

We know that initial value is the point, where, graph intersects y-axis that is when x is equal to 0.

We can see that graph starts at 5000 on y-axis, therefore, initial value is $5000.

The rate of change will be equal to slope of line. Let us find slope of line using points (0,5000) and (1,7500).

$m=\frac{7500-5000}{1-0}$

$m=\frac{2500}{1}$

$m=2500$

Therefore, the rate of change is $2500 per year.

The equation $y=2500x+5000$ represents the amount of money in dollars that Tony expects to deposit in his account.

Answer 2

The equation $\rm y = 2500x+5000$ represents the amount of money in dollars that Tony expects to deposit in his account.

The rate of change is $2500 per year.

Given that,

Tony opens a savings account.

The graph represents the amount of money in dollars.

Tony expects to deposit in his account in terms of the number of years since opening the account.

We have to determine,

The equation represents the amount of money in dollars that Tony expects to deposit in his account and rate of change per year.

According to the question,

The graph that represents the amount of money in dollars that Tony expects to deposit in his account in terms of the number of years since opening the account.

The rate of change and initial value from our given graph.

The initial value is the point, where, graph intersects y-axis that is when x is equal to 0.

The equation represents the amount of money in dollars that Tony expects to deposit in his account is,

$\rm y = 2500x+5000$

The graph starts at 5000 on y-axis, therefore, initial value is $5000.

The rate of change will be equal to slope of line.

Let us find slope of line using points (0,5000) and (1,7500).

Therefore,

The slope of line is,

$\rm m = \dfrac{y_2-y_1}{x_2-x_1}\\\\m = \dfrac{7500-2500}{1-0}\\\\m = 2500$

Hence, the rate of change is $2500 per year.

For more details refer to the link given below.

https://brainly.com/question/17521208