ANSWER CORRECTLY AND IF YOU DONT KNOW IT JUST DONT SAY ANYTHING 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)

9514 1404 393

  A. 40, dollars added per day to the bank account

  B. y -600 = 40(x -0); y = 40x +600; 40x -y = -600

  C. f(x) = 40x +600

  D. $880

Step-by-step explanation:

A. The slope is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (720 -600)/(3 -0) = 120/3

  m = 40

The bank account is increasing at the rate of $40 per day.

__

B. Point-slope form is ...

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

Using the first point, we have (h, k) = (0, 600) and m = 40.

  y -600 = 40(x -0)

Slope-intercept form is ...

  y = mx +b . . . . . . line with slope m and y-intercept b

The first point tells us the y-intercept is b=600, so the equation is ...

  y = 40x +600

Standard form is ...

  ax + by = c . . . . . . . a > 0, and a, b, c mutually prime

This form can be obtained by subtracting y from the point-slope form.

  40x -y = -600

__

C. Replacing y with f(x) in the slope-intercept form gets the desired equation.

  f(x) = 40x +600

__

D. The table shows the balance after 6 days. The balance increases $40 each day, so the balance after 7 days is ...

  $840 +40 = $880 . . . . balance after 7 days