[One Hundred Points if completed.] 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 $600
3 $720
6 $840

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

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

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

Part D: What is the balance in the bank account after 7 days?

Step-by-step explanation:

As per table given, the points are:

(0, 1500), (2, 1350), (4, 1200)

Part A

Slope is found as change in range/change in domain

m = (1350 - 1500)/(2 - 0) = - 150/2 = -75

As per the first point, we have y-intercept of 1500, when x = 0

So the function is:

g(x) = - 75x + 1500

or

y = -75x + 1500

Part B

Slope-intrcept form is given above

Point-slope form:

y - y1 = m(x-x1)

This can be found as per above formula by using a pair of coordinates of one of the points or converted from slope-intercept form:

y - 1500 = - 75(x - 0)

y - 1500 = -75x

Standard form:

Ax + By = C

Converting from the previous equation:

y + 75x = 1500

Part C

The function notation is same as slope-intercept form, where y is substituted with f(x), g(x) or any other notation:

g(x) = -75x + 1500

Part D

Balance after 5 days

x = 5, g(x) = ?

g(5) = -75*5 + 1500 = 1125

After 5 days the balance is going to be $1125

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional