The length of a rectangular garden is three feet less than twice it’s width. if the perimeter of the garden is 42 feet, what is the length?

L = length / W = width / P = Perimeter

L=2W-3 (three feet less than twice its width)

To find a perimeter the formula is 2W+2L=P

So if we have two formulas with the same variables (L & W)

We can substitute one for the other.  In this case we will take L=2w-3 and input it in for "L" in 2W+2L=P.  We know P is 42 so substituting L into the equation will look as such.

2W + 2 ( 2W - 3 ) = 42

2W + 4W - 6 = 42 (Multiply both "2W" & "3" by "2"

6W - 6 = 42 (Add like values)

6W = 48 (Add value to opposite of the equation

W = 8 (Divide each side by 6 to get the value of W)

Now that we have W, we need to take W and substitute it into the first equation, giving us

L = 2 (8) - 3

L = 16 - 3 (PEMDAS)

L = 13 (PEMDAS)

Now that we have both L and W we can plug our answers into the perimeter formula to check our answer.

2 (8) + 2 (13) = 42

16 + 26 = 42 (PEMDAS)

42 = 42 (PEMDAS)

The solution matches meaning the answer is correct.  

the slope of the first function is -3. (3/1)

the slope of the second function is 1. (13-10/6-3).

since |-3| is greater than |1|, the function with the steepest slope is the first.