1. Graphing linear equationsBy
Robert O. Mills Jr.
Hermitage High School
Henrico County Public Schools

2. Part One
Solving for Y

3. In order to graph a linear equation you must first solve for y.

4. Given the Problem :
x+y=4

5. First check to see if y is + or –.
x+y=4
If y is + you leave it alone.

6. What number or factor is on the same side of the equation as + y?
x+y=4

7. Move that number or factor to the other side of the = and change its sign.
x+y=4

8. Move that number or factor to the other side of the = and change its sign.
y=4-x

9. Your answer is:
y=4-x

10. Given the Problem :
x-y=4

11. x-y=4 First check to see if y is + or –.
If y is - you move y to the other side of the = and change it to +y.

12. x-y=4

13. x=4+y

14. What number or factor is on the same side of the equation as + y?
x=4+y

15. Move that number or factor to the other side of the = and change its sign.

16. x = 4 + y

17. x-4 =y
Your answer is:

18. x-4 =y or
y=x-4

19. Given the Problem :
x+2y=4

20. x+2y=4 First check to see if y is + or –.
If y is + you leave it alone.

21. What number or factor is on the same side of the equation as + y?
x+2y=4

22. Move that number or factor to the other side of the = and change its sign.
x+2y=4

23. Move that number or factor to the other side of the = and change its sign.
2y=4-x

24. If the +y factor has a co-efficient it must lose it
If the +y factor has a co-efficient it must lose it. The factors and numbers on the opposite side of the = become a fraction with the y co-efficient as the denominator.
2y=4-x

25. If the +y factor has a co-efficient it must lose it
If the +y factor has a co-efficient it must lose it. The factors and numbers on the opposite side of the = become a fraction with the y co-efficient as the denominator.

26. Given the Problem :
2x-2y=4

27. 2x-2y=4 First check to see if y is + or –.
If y is - you move y to the other side of the = and change it to +y.

28. 2x-2y=4

29. 2x=4+2y

30. What number or factor is on the same side of the equation as + y?
2x=4+2y

31. Move that number or factor to the other side of the = and change its sign.

32. 2x=4+2y

33. 2x-4 =2y
Your answer is:

34. 2x-4 =2y or
2y=2x-4

35. If the +y factor has a co-efficient it must lose it
If the +y factor has a co-efficient it must lose it. The factors and numbers on the opposite side of the = become a fraction with the y co-efficient as the denominator.
2y=2x-4

36. If the +y factor has a co-efficient it must lose it
If the +y factor has a co-efficient it must lose it. The factors and numbers on the opposite side of the = become a fraction with the y co-efficient as the denominator.

37. Advanced Level
There are times when it will be necessary to work the equation to a simpler level.
For example the formula for slope intercept is y = mx + b. Any denominator in this case must be eliminated. How to do this?

38. Most often when we think of the distributive property, we are thinking of using it with ( ) and the operation is multiplication. In the previous example the line is also a grouping tool with the operation division.

40. This is a more complex problem.