Plot 6x-9y=18 on the Cartesian Graph:
Slope intercept form:
Slope intercept form: y = mx + b
y = 0.66666666666667x - 2
Solve the following over the integers
6x - 9y = 18
Use Euclids Algorithm in Rewritten Form:
Calculate the GCF of (6,-9)
Diophantine Table:
| # | Quotient1 | Quotient2 | Remainder1 | Remainder2 | Remainder | Final | Rewritten |
|---|---|---|---|---|---|---|---|
| 1 | 6/-9 | -1 | 6 - (-9 x -1) | 6 - 9 | -3 | 6 = -1 x -9 + -3 | -3 = 6 - -1 x -9 |
| 2 | -9/-3 | 3 | -9 - (-3 x 3) | -9 - -9 | 0 | -9 = 3 x -3 + 0 | 0 = -9 - 3 x -3 |
GCF (6, -9) = -3
Rearrange to solve in terms of GCF = -3
-3 = 6 - -1 x -9
Substitute our rewrite value for
6 - -1()
Multiply the items inside our parentheses by -1
Final Answers
y = 0.66666666666667x - 2
