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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 $1,500
2 $1,350
4 $1,200


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 5 days? (2 points)

Respuesta :

Answer:

Step-by-step

Part A

the slope of the function is-75

Part B

point-slope form is y-1350-75(x - 2)

slope-intercept form is y=-75x + 1500 standard form is 75x + y = 1500

Part C

the function notation of the line is g(x)=-75x + 1500 part d: the balance in the account after 5 days is $1125

g(x) is a linear function, where x is the number of days that have passed and g(x) is the balance in the bank account

at x=0

⇒ g(x) = $1500

at x=2

⇒g(x) = $1350

at x = 4

⇒ g(x) = $1200

Lets consider the points (0,1500), (2,1350), (4,1200) are points lie on the line which represents the function g(x) -the slope of the line which passes through points (x2 y2) explanation:

raphealnwobi

The slope of the line is -$75 per day and the y intercept is $1500.

Linear equation

Linear equation is in the form:

y = mx + b

where y, x are variables, m is the slope of the line (rate of change) and b is the y intercept.

Let g(x) represent  walked in feet after x dayss

From the table, using  the point (0, 1500) and (4, 1200):

[tex]g-g_1=\frac{g_2-g_1}{x_2-x_1} (x-x_1)\\\\g-1500=\frac{1200-1500}{4-0} (x-0)\\\\g(x)=-75x+1500[/tex]

The slope of the line is -$75 per day and the y intercept is $1500.

After 5 days:

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

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