Question

HELP ME ASAP!!!!!!!!!!!! 30 POINT REWARD!!!!!!!!!!!!!!!!!!!!!!!PLEASE EXPLAIN AND SOLVE!!!!!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 intepret the slope of the function
Part B: Write the equation in point slope, slope intercept form, and standard form
Part C: Write the equation of the line using function notation
Part D: What is the balance of the bank account after 7 days?

Answer 1

Part A:

The y-intercept is $1,500

The x-intercept is 20 days

Part B:

Equation of the line in point-slope form is y - 1350 = -75×(x - 2)

Equation of the line in slope-intercept form is y = -75·x + 1500

Equation of the line in standard form is y + 75·x = 1500

Part C:

f(x) = -75·x + 1500

Part D:

$1,125

Explanation:

The information given are;

x, g(x)

0, $1,500

2, $1,350

4, $1,200

The equation of a straight line relation between the x, and y, coordinates in slope and intercept form is y = m·x + c

Where;

m = The slope

c = The y-intercept

From the data, we have two points, (x₁, y₁), (x₂, y₂) given as (0, 1,500), (2, 1350);

The y-intercept = y at x = 0 = 1,500

y = -75·x + 1500

x = 1500/75 = 20

Part B:

The equation in point-slope form is y - y₁ = m×(x - x₁)

Which gives;

Equation of the line in point-slope form is y - 1350 = -75×(x - 2)

Equation of the line in slope-intercept form is y = -75·x + 1500

Equation of the line in standard form is y + 75·x = 1500

Part C:

The equation of the line using function notation is f(x) = -75·x + 1500

Part D:

The balance in the bank after 5 days is f(5) = -75 × 5 + 1500 = $1,125