Solve for

1
Solve for y for each

• 1.) 2x y 9 2.) -x y 3
• 3.) y 4 3x 4.) 2 y ?x
• 5.) 7x y -8 6.) y 1 -3x

-2x -2x
- 3 - 3
y -2x 9
y -x - 3
?x ?x
4 4
y 3x 4
y ?x 2
-7x -7x
1 1
-y -7x - 8
y 7x 8
y -3x 1
2
Again, solve for y

• 1.) 2x 2y 10 2.) 6x 3y -3
• 3.) 2y 7 -x 4.) 15x 5y 20

- 2x - 2x
- 6x - 6x
-3y -6x - 3
2y -2x 10
Divide by 2
Divide by -3
-3 -3 -3
y -x 5
y 2x 1
7 7
- 15x - 15x
2y -1x 7
5y -15x 20
Divide by 2
Divide by 5
y -½x 3.5
y -3x 4
3
PLOTTING POINTS
Remember when plotting points you always start at
the origin. Next you go left (if x-coordinate is
negative) or right (if x-coordinate is positive.
Then you go up (if y-coordinate is positive) or
down (if y-coordinate is negative)
B
C
A
D
Plot these 4 points A (3, -4), B (5, 6), C (-4,
5) and D (-7, -5)
4
4.2 Graphing Linear Equations
5
Linear Equation

• An equation for which the graph is a STRAIGHT
  line

NO FRACTIONS and NO LEADING NEGATIVES!!!
6

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.
7
What is a Linear Equation?
A linear equation is an equation whose graph is a
LINE.
8
What is a Linear Equation?
The equations we will be graphing have two
variables, x and y.
For example,
A solution to the equation is any ordered pair (x
, y) that makes the equation true.
The ordered pair (3 , 2) is a solution since,
If we were to plot all these ordered pairs on a
graph, we would be graphing a line.
9
Solution

• 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
10
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
11
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

12
Linear Equation

• Example
• y x 3

13
Graphing

• Step 1
• T-Chart
• Choose some values for x, and make a t-chart

14
Graphing

• Step 2
• Find solutions using table

y x 3
x y
-2
-1
0
1
2
3
x y
-2 1
-1 2
0 3
1 4
2 5
3 6
Create these ordered pairs
(-2,1) and (-1,2) and (0,3) and (1,4) and (2,5)
and (3,6)


15
Graphing

• Step 3
• Graph the points from the table
• (-2,1) (-1,2) (0,3) (1,4) (2,5)

16
Graphing

• Step 4
• 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
17

• 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.
18

• Use the x-values -2, -1, 0, 1, and 2

-2 -1 0 1 2
5 4 3 2 1
19

• With your table completed for three sets of
  values, you are ready to graph the line.

y -x 3
-2 -1 0 1 2
5 4 3 2 1
20
Graphing a Linear Equation
How do we graph linear equations?
Lets try this one y 3x 2
Make a Table of values
x y
2
1
0
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
21
Graphing a Linear Equation
How about another one!
Lets 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
0
2
4
-5
½(-4) 3 -5
-4
½(-2) 3 -4
-3
½(-0) 3 -3
-2
-1
22
Create a table of values for each equation, and
graph it on grid paper
1.
2.
x y
-2 3
-1 4
0 5
1 6
2 7
3 8
x y
-2 11
-1 9
0 7
1 5
2 3
3 1
y x 5
y -2 x 7
3.
x y
-4 -1
-2 0
0 1
2 2
4 3
6 4
x y
-2 -8
-1 -6
0 -4
1 -2
2 0
3 2
4.
23
Try These

• Make a table for each function using x-valuse -2,
  -1, 0, 1, 2, 3
• y 2x 3 2) y -x - 4

x y
-2 -1
-1 1
0 3
1 5
2 7
3 9
x y
-2 -2
-1 -3
0 -4
1 -5
2 -6
3 -7
24
Find some solutions of this linear equations

• 1.) -2x y -3

First Solve for y
y 2x - 3
x y
-1 -5
0 -3
1 -1
2 1
3 3
Use the x-values of -1, 0, 1, 2 and 3
25
Make a t-chart for this function

• 1.) -4x y -1

26
Graph the function y 3x -2

• First make a t-chart

27
Graph the function 4y 2x 8

• First solve for y

• 4y 2x 8
• 2x 2x
• 4y 2x 8
• 4 4
• y ½x 2

x y
-4 0
-2 1
0 2
2 3
4 4
6 5
Then use which x-values???
28
Graph the function 3x 2y 6

• First solve for y

• 3x 2y 6
• -3x -3x
• -2y -3x 6
• -2 -2 -2
• y 3/2 x - 3

x y
-4 -9
-2 -6
0 -3
2 0
4 3
6 6
Then use which x-values???
29
Graph the equationy 2x 6
30
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.
31
Parts of a Coordinate Plane








QUADRANT II (-x, y)
QUADRANT I (x, y)
Origin
QUADRANT III (-x, -y)
QUADRANT IV (x, -y)
X-Axis
Y-Axis
32
State the quadrant in which each ordered pair is
located.

• 1.) (7,-3)
• 2.) (6,0.7)
• 3.) (0,-3)
• 4.) (-2,-2)
• 5.) (-3,9)
• 6.) (½,0)

IV
I
On y-axis, not in any quadrant
III
II
On x-axis, not in any quadrant
33
Fill in the blanks

• Name the point with coordinates (0,0) at the
  intersection of the x and y axis ___________
• Name the vertical axis ___________
• Name the horizontal axis ___________
• What does the graph of a linear equation look
  like? _____________

ORIGIN
y-axis
x-axis
Straight line
34
X-intercept Y-intercept

• The x-intercept has a y coordinate of ZERO

35
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)