using slope and y intercept

Question

The equation that describes the amount of garbage in a landfill site is G=4000 + 300d, where G stands for the amount of garbage measured in tonnes and d stands for the number of days starting from now. How would a graph and table look in this situation and word description. 

Also from this question I can't figure out 

1. how i would get the slope and y intercept from this on a graph? 
2. the initial value and the first differences 
3. the initial value and rate of change for the word description

Answer 1

The equation of a line is:

 

y = mx + b

 

where m = the slope of the line and b = the y-intercept.  Your equation is:

 

G = 4000+ 300d

 

Rearranging:

 

G = 300d + 4000

 

Here we use d instead of x and G instead of y, but it is the equation of a straight line with slope m = 300 and y-intercept = 4000.  The initial value occurs when d = 0:

 

G(d=0) = 300*0 + 4000 = 4000   (start, day 0))

G(d=1) = 300*1 + 4000 = 4300   (day 1)

G(d=2) = 300*2 + 4000 = 4600   (day 2)

etc.

 

The rate of change is just the slope, m = 300 tonnes per day, which you can see when you look at the values of G for d = 0, 1, and 2.