Question

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)

Answer 1

Answer:

A)m = Slope = 15

B)Point slope form :$y-325=15(x-0)$

Slope intercept form: y=15x+325

Standard forms: 15x-y+325=0

C)f(x)=15x+325

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

Step-by-step explanation:

x            g(x)

0           $325

5           $400

10          $475

x: number of days that have passed

g(x) : the balance in the bank account:

We will use two point slope form to find equation

$(x_1,y_1)=(0,325)\\(x_2,y_2)=(5,400)\\y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\y-325=\frac{400-325}{5-0}(x-0)\\y-325=15x\\y=15x+325$

A)

General equation of line = y = mx+c

Where m is slope of function

On comparing with y=15x+325

m = Slope = 15

B)

Point slope form :$y-325=\frac{400-325}{5-0}(x-0)=y-325=15(x-0)$

Slope intercept form: y=15x+325

Standard forms: 15x-y+325=0

C)f(x)=15x+325

Where f(x) : the balance in the bank account after x days

x: number of days that have passed

D)

Balance in the bank account after 12 days

f(12)=15(12)+325=505