Geometry
13.6 Graphing Linear Equations
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
0
4
8
y
3
0
-3
.
(0, 3)
.
(4, 0)
.
(8, -3)
II. Standard Form: (Ax + By = C). Getting x and y intercepts: (x, 0) and (0, y)
1) 2x + 3y = 6
x
y
0
3
2
0
2) 6x + 7y = 4
x
Try the cover up method!!!
.
(0, 2)
.
(3, 0)
0
2/3
3
y
4/7
0
-2
Not too accurate…
Plug in another point!!!
..
(0, 4/7)
(2/3, 0)
.
(3, -2)
II. Slope-Intercept Form (y = mx + b):
m = slope;
b = y-intercept
2. y  1 x  4
1. y = 2x – 3
.
..
.
..
.
.
.
.
2
..
.
.
..
(0, 4)
(0, -3)
3. x = 3
xertical
Why?
(3, 5)
(3, 1)
4. y = 2
Why?
(3, -4)
(3, -7)
Thus x=3!!
. .
yorizontal (-6, 2) (-1, 2)
Thus y=2!!
.
(6, 2)
III. Finding Slope-Intercept Form: (y = mx + b)
2) 3x – 4y = 10
-3x
-3x
1. 2x + y = 6
-2x
-2x
y = -2x + 6
m = _____
-2
b = _____
6
m = _____
-3/4
b = _____
5/2
4. x – 2y = 4y + 1
-4y -4y
x – 6y = 1
-x
-x
-6y = -x + 1
-6
-6
-6
y = 1/6x – 1/6
3. x = y
y=x
1
m = _____
-4y = -3x + 10
-4
-4
-4
y = 3/4x – 5/2
0
b = _____
1/6
m = _____
-1/6
b = _____
IV. Systems of Equations:
Two lines in a coordinate plane can do two things:
(1) intersect (perpendicular or not)
(2) not intersect (parallel)
Systems
By Substitution
2x +(y)= 8
y =( 2x)
Isolate a variable first.
This is already done.
Then substitute.
Algebraic
2x + (2x) = 8
4x = 8
x=2
Graph
.
(2,4)
Substitute 2 back in for x in
the easier equation!!
y = 2x
y = 2(2)
y=4
The solution to the system is (2, 4)
Graph 2x + y = 8
-2x
-2x
y = -2x + 8
Graph y = 2x
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
By Addition
x – 6y = -3
3x + 6y = 15
4x
= 12
x=3
Graph
3(3) + 6y = 15
9 + 6y = 15
-9
-9
6y = 6
y=1
Substitute 3 back in for x in
the easier equation!!
The solution to the system is (3, 1)
.
(3,1)
Graph x – 6y = -3
-x
-x
-6y = -x – 3
Graph 3x + 6y = 15
-6
-6 -6
-3x
-3x
y = 1/6x + 1/2
6y = -3x + 15
6
6
6
y = -1/2x + 5/2
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
By Addition w/Multiplication
4x + 2y = 12
(2x + y = 6 )2
3x – 2y = 2
7x
= 14
x=2
Graph
.
4(2) + 2y = 12
8 + 2y = 12
-8
-8
2y = 4
y=2
Substitute 2 back in for x in
the easier equation!!
The solution to the system is (2, 2)
(2,2)
Graph 2x + y = 6
-2x
-2x
y = -2x + 6
Graph 3x – 2y = 2
-3x
-3x
-2y = -3x + 2
-2
-2 -2
y = 3/2x – 1
Solve the following systems of equations.
1. 2x + y = 8
3x – y = 2
(2,4)
2. x – 6y = –3
3x + 6y = 15
(3,1)
3. 2x + y = 6
3x – 2y = 2
(2,2)
4. 2x + y = –2
2x – 3y = 14
(1,-4)
Note: After you solve, you can always plug in your solution to check.
HW

Next time you debate on doing something
good, do it!