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)

The balance in the bank account after 12 days is $505.

Step-by-step explanation:

The data provided is as follows:

Number of Days (x)     Balance [g (x)]

             0                          $325

             5                          $400

            10                          $475

(a)

Compute the slope as follows:

Thus, the slope of the function is 15.

The slope of a line is the rate of change in one variables that is caused by a unit change in the other variable.

In this case, the slope of the line implies that when one day has passed the balance in the bank account is increased by $15.

(b)

The point-slope form of the line is:

Consider the point (0, 325)

The point-slope form is, y = 15 (x - 325)

Compute the intercept as follows:

The slope intercept form of the line is:

The standard form of the line is:

(c)

The equation of the line using function notation is:

(d)

Compute the value of g (x) when x = 12 as follows:

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

A)The slope of function is 15

B)  Point slope form :

Slope-intercept form : y=15x+325

Standard form: 15x+y=325

C)g(x)=15x+325

D) The balance in the bank account after 12 days is $505  

Step-by-step explanation:

x                     g(x)

0                    $325

5                    $400

10                  $475

Part A: Find and interpret the slope of the function.

Formula of slope =

We are given that

Substitute the values in the formula:

m=15

So, The slope of function is 15

Part B: Write the equation of the line in point-slope, slope-intercept, and standard forms.

Point slope form :

Slope-intercept form =

Standard form :

So,

Part C: Write the equation of the line using function notation.

Part D:  What is the balance in the bank account after 12 days?

Substitute x = 12

So,

Hence the balance in the bank account after 12 days is $505