How do you know if an expression can be factored using GCF and not one of the other methods

The table is:

Number of washes denoted by x: 0, 8, 12

Amount left on card denoted by y: 30, 18, 12

a.       Write an equation that shows the amount of dollars left on the card

Solution:

18 – 30 divided by 8 – 0 = -12/8

On simplest form is -3/2

The equation is y = -3/2x + 30

b.      Explain the meaning of the negative slope above.

As the number of car washes increase, the dollars left on the card decreases.

c.       What is the maximum value of x?

0 = -3/2x + 30

2/3 x 3/2 x = 30/1 x 2/3

Cancel 2/3 x 3/2 and reduce 30 by 3 we get 10, 10 x 2

x = 20