1. Solve for “y” for each:
1.) 2x + y = 9 2.) -x = y ) 2y – 4 = 3x 4.) 2 = y – ⅓x 5.) 7x – y = -8 6.) 3y – 1 = -3x
-2x x
y = -2x + 9
y = -x - 3
+⅓x ⅓x
2y = 3x + 4
y = ⅓x + 2
-7x x
-y = -7x - 8
y = 7x + 8
3y = -3x + 1

2. Again, solve for “y”
1.) 2x + 2y = 10 2.) 6x – 3y = -3 3.) 2y – 7 = -x 4.) 15x + 5y = 20
- 2x x
- 6x x
-3y = -6x - 3
2y = -2x + 10
Divide by 2
Divide by -3
y = -x + 5
y = 2x + 1
- 15x x
2y = -1x + 7
5y = -15x + 20
Divide by 2
Divide by 5
y = -½x + 3.5
y = -3x + 4

3. 3.3 Graphing Linear Equations

4. Linear Equation An equation for which the graph is a STRAIGHT line
NO FRACTIONS and NO LEADING NEGATIVES!!!

5. Linear Equation: an equation whose graph forms a line.
In linear equations, all variables are taken to the first power.
is linear.
Why?
is not.

6. What is a Linear Equation?y x
Linear
A linear equation is an equation whose graph is a LINE.
Not Linear

7. Solution INFINITE AMOUNT OF SOLUTIONS (x,y)
Any ordered pair of numbers that makes a linear equation true.
FOR: y = x - 9
(9,0) IS ONE SOLUTION
(x,y)
Can you think of another solution?
Is (11,2)??
INFINITE AMOUNT OF SOLUTIONS
Yes
Is (-5,-14)??
Yes

8. Determine if the ordered pair given is a solution of x + 2y = 5
1.) (1,2) 2.) (7,-3)
(1) + 2(2) = 5??
(7) + 2(-3) = 5??
5 = 5
1 = 5 NO
YES

9. Steps to GRAPHING
1.) SOLVE FOR “y” 2.) MAKE A T-CHART 3.) GRAPH EACH ORDERED PAIR 4.) CONNECT THE DOTS TO DRAW THE LINE

10. Linear Equation
Example:
y = x + 3

11. Find solutions using table
Graphing
Find solutions using table
y = x + 3 x y -2 -1 1 2 3 x y -2 1 -1 2 3 4 5 6
Create these ordered pairs
(-2,1) and (-1,2) and (0,3)
and (1,4) and (2,5) and (3,6)

12. Graphing Graph the points from the table
(-2,1) (-1,2) (0,3) (1,4) (2,5)

13. Graphing
Draw a line to connect them
So by looking at this line we can assume that (5,8) is a solution?
What other points can we conclude is a solution???
y = x +3

14. Then creating a table of values.
Suppose you were asked to graph the solution set of the linear equation,
x + y = 3
-x x
y = -x + 3
FIRST SOLVE FOR Y!!
Then creating a table of values.

15. Use the x-values -2, -1, 0, 1, and 2

16. With your table completed for three sets of values, you are ready to graph the line.
y = -x + 3

17. Graphing a Linear Equationy x
How do we graph linear equations?
Let’s try this one: y = 3x – 2
Make a Table of values x y –2 –1 1 2 –8
y = 3(–2) – 2 = –8 –5
y = 3(–1) – 2 = –5 –2
y = 3(0) – 2 = –2 1
y = 3(1) – 2 = 1 4
y = 3(2) – 2 = 4

18. Graphing a Linear Equationy x
How about another one!
Let’s try x – 2y = 6.
First Step:
Solve for y
x – 2y = 6
–2y = -x + 6
y = ½x - 3
Second Step: Make a t-chart x y –4 –2 2 4 -5
½(-4) – 3 = -5 -4
½(-2) – 3 = -4 -3
½(-0) – 3 = -3 -2 -1

19. Create a table of values for each equation, and graph it on grid paper:1. x y -2 3 -1 4 5 1 6 2 7 8 2. x y -2 11 -1 9 7 1 5 2 3
y = x + 5
y =-2 x + 7 3. x y -2 -8 -1 -6 -4 1 2 3 x y -4 -1 -2 1 2 4 3 6 4.

20. Make a table for each function using x-valuse -2, -1, 0, 1, 2, 3:
Try These
Make a table for each function using x-valuse -2, -1, 0, 1, 2, 3:
y = 2x ) y = -x - 4 x y -2 -1 1 3 5 2 7 9 x y -2 -1 -3 -4 1 -5 2 -6 3 -7

21. Find some solutions of this linear equations
1.) -2x + y = -3
First Solve for y
y = 2x - 3 x y -1 -5 -3 1 2 3
Use the x-values of
-1, 0, 1, 2 and 3

22. Make a t-chart for this function:
1.) -4x + y = -1

23. Graph the function y = 3x -2
First make a t-chart

24. Graph the function: 4y – 2x = 8
First solve for “y”
4y – 2x = 8
+2x x
4y = 2x + 8
y = ½x + 2 x y -4 -2 1 2 3 4 6 5
Then use which x-values???

25. Graph the function: 3x – 2y = 6
First solve for “y”
3x – 2y = 6
-3x x
-2y = -3x + 6
y = 3/2 x - 3 x y -4 -9 -2 -6 -3 2 4 3 6
Then use which x-values???

26. Graph the equation y = 2x + 6

27. Graph the equation: -6x + 2y = 4
y = 3x + 2
Plot (-2, -4), (0, 2) and (1, 5)
Then draw the line. Make sure your line covers the graph and has arrows on both ends. Be sure to use a ruler.

28. Which ordered pair does NOT satisfy the equation
2x + y = 7?
Which ordered is a solution of the equation
5x – 3y = 17?
a.) (4,1)
b.) (1,4)
c.) (5,1)
d.) (1,5)
a.) (1,5)
b.) (3,2)
c.) (0,7)
d.) (4,-1)