1. refer to the equation 4x – 2y = 12 (a) create a table of values for at least 4 points. show your work. (b) use the table of values to graph the line

Refer to the equation 4x – 2y = 12

To make a table we need to solve for y

4x – 2y = 12

Subtract 4x on both sides

-2y = -4x + 12

Now divide the whole equation by -2

y = 2x - 6

Now we assume 4 values for x  and find out y to make a table

x            y = 2x-6

0           y= 2(0) -6 = -6

1           y= 2(1) -6 = -4

2           y= 2(2) -6 = -2

3           y= 2(3) -6 = 0

We got 4 points (0,-6) (1,-4) (2,-2) and (3,0)

Use the table and graph the line

Graph is attached below

Part A. The standard form of a rate equation is:

 y = Ao (1 + r)^x

Where,

Ao = represents the initial value

r = represents the rate of growth

Therefore rewriting the given f(x) equation in this form:

f(x) = 2.96 (1 + 0.04)^x

r = 0.04 = 4%

Hence, the price of fuel A is increasing each month by 4%.

We can prove this by assuming two values of x = 1 and 2 and getting the ratio:

f(x=2) / f(x=1) = 2.96(1.04)^2 / 2.96(1.04) = 1.04

Since ratio is 1.04, therefore there is in fact a 4% increase.

Part B. To determine the growth rate of fuel B, let us take the ratio of months 1 and 2.

3.22 / 3.04 = 1.06

r = 0.6 = 6%

Therefore the fuel with a greater percentage change in price per month is fuel B.