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. (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 7 days? (2 points)

Part A)  (see the explanation)

Part B)

1) point-slope form --->  

2) slope-intercept form --->

3) standard form >

Part C)

Part D)

Step-by-step explanation:

Part A: Find and interpret the slope of the function

Let

x > is the number of days

g(x) --->  is the balance in the bank account

we know that

The formula to calculate the slope between two points is equal to

take two ordered pairs from the data of the table of values

(0,600) and (3,720)

substitute in the formula

That means that the balance in the bank account increases $40 each day

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

step 1

Find the equation in point-slope form

we have

substitute

step 2

slope-intercept form

Isolate the variable y

Adds 600 both sides

step 3

standard form

The equation of the line in standard form is equal to

where

A is a positive integer

B and C are integers

we have

subtract y both sides

subtract 600 both sides

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

we have

Let

g(x)=y

so

---> equation in function notation

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

For x=7 days

substitute in the linear equation

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°