The table of values represents a linear function g(x), where x is the number of days that have passed and g(x) is the balance in the bank account: x g(x) 0 $325 5 $400 10 $475 Part A: Find and interpret the slope of the function. (3 points) Part B: Write the equation of the line in point-slope, slope-intercept, and standard forms. (3 points) Part C: Write the equation of the line using function notation. (2 points) Part D: What is the balance in the bank account after 12 days? (2 points)

Part A)

The slope m is 15.

This means that $15 is deposited into the bank account each day.

Part B)

Point-slope form:

Slope-intercept form:

Standard Form:

Part C)

Part D)

After 12 days, the balance of the bank account will be $505.

Step-by-step explanation:

We are given a table of values that lists x, the number of days that have passed, and g(x), the balance of the bank account.

The table represents a linear function.

Part A)

To find the slope, we can use the slope formula:

Where (x₁, y₁) and (x₂, y₂) are two points.

So, let’s pick two points from our table. We can use (0, 325) and (5, 400).

Let (0, 325) be (x₁, y₁) and let (5, 400) be (x₂, y₂). Substitute the values into the slope formula:

Evaluate:

So, the slope is 15 (or, more precisely, 15/1).

This means that $15 gets deposited into the bank account each day.

Part B)

We want to write the equation of the line in point-slope form, slope-intercept form, and standard form.

A) Point-slope form is given by:

Where m is the slope and (x₁, y₁) is a point.

We will substitute 15 for m.

We can use any point, but let’s use (0, 325) for (x₁, y₁) for consistency. Hence:

And this is point-slope form. You may choose to simplify the zero.  

For reference, here are the other two forms possible given the table:

B) Slope-intercept form is given by:

Where m is the slope and b is the y-intercept.

Remember that the y-intercept is where x=0.

From our table, we can see that when x=0, y=325.

Therefore, our y-intercept is 325.

So, we will substitute 325 for b.

And we will also substitute 15 for m. Therefore:

C) Standard form is given by:

Where A, B, and C are integers, and A is positive.

We can start with the slope-intercept form:

And convert this to standard form. Subtract 15x from both sides:

Since A should be positive, multiply everything by -1. Hence:

Part C)

We can use the slope-intercept form:

Since our dependent variable, y, is the output of our function, y is the same as g(x).

Therefore, we can substitute g(x) for y to acquire:

Part D)

We can use our function. We want to find the balance after 12 days. Hence x=12.

Therefore:

Evaluate:

After 12 days, the balance in the bank account is $505.

describing distributions is one of the key skills you’ll need to earn a high score on the ap statistics exam. if you need proof of this, just flip through some past exam questions, which can be found at the collegeboard website. you’ll notice that the first free response question is almost always a question requiring you to look at a graph and describe it.

step-by-step explanation: just trying to get points sorry : (

answer: he is 272195

step-by-step explanation: all you have to do is multiple 3535 and 77 and it equals 272195