1. Graph Linear Systems Written in Standard Form

2. Types of Linear Equations
Slope Intercept Form: y = mx + b
You have used this one the most.
If you have your slope and y-intercept, you 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)

3. What type of Equation is this?
y = 2x -9
3x – 4y = 18
-x + 19y = 5
y = ½ x + 4
14x + y = 3
y = -2/3x – 9/2
Slope-Intercept Form
Standard Form

4. Standard Form: Ax + By = C
To graph an equation in standard form, you use the x- and y-intercepts.
The x-intercept is: “What is x if y is zero?” (# , 0)
The y-intercept is: “What is y if x is zero?” (0, #)

5. Find the x- and y- intercepts of the following equations:
4x + 2y = 12
3x – y = 6
-5x + 4y = 20
9x – 12y = -36
(3, 0) & (0, 6)
(2, 0) & (0, -6)
(-4, 0) & (0, 5)
(-4, 0) & (0, 3)

6. It is where the two lines intersect.
What does “Solving a Linear System” mean?
It is where the two lines intersect.

7. Graph to solve the linear system.
2x – y = 2
4x + 3y = 24
Since the equations are in standard form, find the x- and y-intercepts to graph.
2x – y = 2
2x – 0 = 2
2x = 2
x = (1, 0)
2(0) – y = 2
-y = 2
y = (0, -2)
4x + 3y = 24
4x + 3(0) = 24
4x = 24
x = (6, 0)
4(0) + 3y = 24
3y = 24
y = (0, 8)

8. Graph to solve the linear system.
2x – y = 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.

9. Graph to solve the linear system.
-4x – 2y = -12
4x + 8y = -24
Since the equations are in standard form, find the x- and y-intercepts to graph.
-4x – 2y = -12
-4x – 2(0) = -12
-4x = -12
x = (3, 0)
-4(0) – 2y = -12
-2y = -12
y = (0, 6)
4x + 8y = -24
4x + 8(0) = -24
4x = -24
x = (-6, 0)
4(0) + 8y = -24
8y = -24
y = (0, -3)

10. Graph to solve the linear system.
-4x – 2y = -12 Intercepts are (3, 0) & (0, 6)
4x + 8y = Intercepts are (-6, 0) & (0, -3)
Where do the lines intersect?
(6, -6) is the solution to this system of linear equations.