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
part b: write the equation of the line in point-slope, slope intercept, and standard forms
part c: write the equation of the line using function notation
part d: what is the balance in the bank account after 7 days?

a) slope is the change in y over the change in x:

change in y = 840 - 600 = 240

change in x = 6-0 = 6

slope = 240 / 6

slope = 40

b)   point slope form is written as y -y1 = m(x-x1)

m is the slope found in part a.

point slope form = y - 600 = 40(x-0)

slope intercept form is written as y = mx +b

where m is the slope found in part a and b is the y intercept, which is the value of y when x is 0

slope intercept form = y = 40x+600

standard form is written as ax +by = c where a is the slope, b is the valoe of x in the y-intercept and cis the negative value of the y-intercept

standard form = 40x - y = -600

c) function notation changes the y to f(x) using the slope intercept form y = 40x +600 change y to f(x):

f(x) = 40x +600

d) replace x with 7 and solve :

y = 40(7) +600 = 280 + 600 = $880