1. 13.6 Graphing Linear Equations
Geometry
13.6 Graphing Linear Equations

2. Graph on coordinate plane by using a t-chart
Graph on coordinate plane by using a t-chart. Try to pick values of x that will
give you integers.
1) 3x + 4y = 12 x y 3
.(0, 3) 4 .
(4, 0) 8 -3 .
(8, -3)

3. II. Standard Form: (Ax + By = C)
II. Standard Form: (Ax + By = C). Getting x and y intercepts: (x, 0) and (0, y)
1) 2x + 3y = 6
2) 6x + 7y = 4 x y x y
Try the cover up method!!!
4/7 2
Not too accurate…
Plug in another point!!!
2/3 3 3 -2
.(0, 2)
.(0, 4/7) .
(3, 0) .
(2/3, 0)
.(3, -2)

4. II. Slope-Intercept Form (y = mx + b):
m = slope; b = y-intercept
y = 2x – 3
3. x = 3
4. y = 2 . . . 2.
.(0, 4) . . . . .
.(0, -3) . .
.(3, 5) . . .
.(3, 1)
xertical
yorizontal
(-6, 2)
(-1, 2)
(6, 2)
Why?
Why?
.(3, -4)
.(3, -7)
Thus y=2!!
Thus x=3!!

5. III. Finding Slope-Intercept Form: (y = mx + b)
1. 2x + y = 6
m = _____ b = _____
2) 3x – 4y = 10
3. x = y
4. x – 2y = 4y + 1
-2x
-2x
-3x
-3x
y = -2x + 6
-4y = -3x + 10 -4 -4 -4
y = 3/4x – 5/2 -2 6
-3/4
5/2
-4y
-4y
y = x
x – 6y = 1 -x -x
-6y = -x + 1 -6 -6 -6
y = 1/6x – 1/6 1
1/6
-1/6

6. .(2,4) IV. Systems of Equations:
Two lines in a coordinate plane can do two things:
(1) intersect (perpendicular or not) (2) not intersect (parallel)
Systems
Algebraic
Graph
By Substitution
2x + y = 8
y = 2x
.(2,4)
2x + (2x) = 8
( )
( )
4x = 8
x = 2
y = -2x + 8
Substitute 2 back in for x in
the easier equation!!
Isolate a variable first.
This is already done.
Then substitute.
y = 2x
y = 2x
Graph 2x + y = 8
y = 2(2)
-2x x
y = 4
y = -2x + 8
The solution to the system is (2, 4)
Graph y = 2x

7. . IV. Systems of Equations:
Two lines in a coordinate plane can do two things:
(1) intersect (perpendicular or not) (2) not intersect (parallel)
Systems
Algebraic
Graph
By Addition
x – 6y = -3
3x + 6y = 15
3(3) + 6y = 15
y = -1/2x + 5/2 .
(3,1)
9 + 6y = 15
y = 1/6x + 1/2
4x = 12
6y = 6
x = 3
y = 1
Substitute 3 back in for x in
the easier equation!!
Graph x – 6y = -3
The solution to the system is (3, 1)
-x x
-6y = -x – 3
Graph 3x + 6y = 15
-3x x
y = 1/6x + 1/2
6y = -3x + 15
y = -1/2x + 5/2

8. . IV. Systems of Equations:
Two lines in a coordinate plane can do two things:
(1) intersect (perpendicular or not) (2) not intersect (parallel)
Systems
Algebraic
Graph
By Addition w/Multiplication
2x + y = 6
3x – 2y = 2
4(2) + 2y = 12 .
(2,2)
4x + 2y = 12
( )2
8 + 2y = 12
2y = 4
7x = 14
y = 3/2x – 1
y = 2
y = -2x + 6
x = 2
Substitute 2 back in for x in
the easier equation!!
Graph 2x + y = 6
The solution to the system is (2, 2)
-2x x
y = -2x + 6
Graph 3x – 2y = 2
-3x x
-2y = -3x + 2
y = 3/2x – 1

9. 1. 2x + y = 8 3x – y = 2 2. x – 6y = –3 3x + 6y = 15 3. 2x + y = 6
Solve the following systems of equations.
1. 2x + y = 8
3x – y = 2
2. x – 6y = –3
3x + 6y = 15
3. 2x + y = 6
3x – 2y = 2
4. 2x + y = –2
2x – 3y = 14
(2,4)
(3,1)
(2,2)
(1,-4)
Note: After you solve, you can always plug in your solution to check.

10. HW
Next time you debate on doing something good, do it!