Transcript Graph Linear Systems Written in Standard Form

Graph Linear Systems
Written in Standard
Form
Types of Linear Equations
O Slope Intercept Form: y = mx + b
O You have used this one the most.
O If you have your slope and y-intercept, you
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can graph a line or even a system of
equations (two lines).
Standard Form: Ax + By = C
“A” is the coefficient of “x.”
“B” is the coefficient of “y.”
“C” is a number (a constant)
What type of Equation is this?
1. y = 2x -9
1. Slope-Intercept Form
2. 3x – 4y = 18
2. Standard Form
3. -x + 19y = 5
3. Standard Form
4. y = ½ x + 4
4. Slope-Intercept Form
5. 14x + y = 3
5. Standard Form
6. y = -2/3x – 9/2
6. Slope-Intercept Form
Standard Form: Ax + By = C
O To graph an equation in standard form, you
use the x- and y-intercepts.
O The x-intercept is: “What is x if y is zero?”
(# , 0)
O The y-intercept is: “What is y if x is zero?”
(0, #)
Find the x- and y- intercepts of
the following equations:
1. 4x + 2y = 12
1. (3, 0) & (0, 6)
2. 3x – y = 6
2. (2, 0) & (0, -6)
3. -5x + 4y = 20
3. (-4, 0) & (0, 5)
4. 9x – 12y = -36
4. (-4, 0) & (0, 3)
What does “Solving a
Linear System” mean?
It is where the two lines
intersect.
Graph to solve the linear
system.
2x – y = 2
4x + 3y = 24
O Since the
equations are in
standard form,
find the x- and yintercepts to
graph.
2x – y = 2
2x – 0 = 2
2x = 2
x=1
(1, 0)
4x + 3y = 24
4x + 3(0) = 24
4x = 24
x = 6 (6, 0)
2x – y = 2
2(0) – y = 2
-y = 2
y = -2
(0, -2)
4x + 3y = 24
4(0) + 3y = 24
3y = 24
y = 8 (0, 8)
Graph to solve the linear
system.
2x – y = 2 Intercepts are (1, 0) & (0, -2)
4x + 3y = 24 Intercepts are (6, 0) & (0, 8)
Where do the lines
intersect?
(3, 4) is the
solution to
this system
of linear
equations.
Graph to solve the linear
system.
-4x – 2y = -12
4x + 8y = -24
O Since the
equations are in
standard form,
find the x- and yintercepts to
graph.
-4x – 2y = -12
-4x – 2(0) = -12
-4x = -12
x=3
(3, 0)
4x + 8y = -24
4x + 8(0) = -24
4x = -24
x = -6 (-6, 0)
-4x – 2y = -12
-4(0) – 2y = -12
-2y = -12
y=6
(0, 6)
4x + 8y = -24
4(0) + 8y = -24
8y = -24
y = -3 (0, -3)
Graph to solve the linear
system.
-4x – 2y = -12 Intercepts are (3, 0) & (0, 6)
4x + 8y = -24 Intercepts are (-6, 0) & (0, -3)
Where do the lines
intersect?
(6, -6) is the
solution to
this system
of linear
equations.