1. Graphing Linear Equations
Dr. Fowler  CCM
Graphing Linear Equations
Point slope
x & y intercepts
Pick 3 points

2. Linear means of a line. So a linear equation is the equation of a line
Linear means of a line. So a linear equation is the equation of a line. In linear equations, all variables are to the first power.
is linear.

3. 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

4. Graphing Ordered Pairs on a Cartesian Plane
Write the Steps: 1) Begin at the origin
y-axis
2) Use the x-coordinate to move right (+) or left (-) on the x-axis
3) From that position move either up(+) or down(-) according to the y-coordinate
Origin
(6,0)
x- axis
4) Place a dot to indicate a point on the plane
Examples: (0,-4)
(6, 0)
(-3,-6)
(0,-4)
(-3, -6)

5. Graph using slope & y-intercept
Slope-Intercept Form
y = mx + b
m = slope
b = y-intercept
Graph using slope & y-intercept

6. Standard Form
ax + by = c
Graph using
x & y intercepts

7. Graphing with slope-intercept
Start by graphing the y-intercept (b = 2).
From the y-intercept, apply “rise over run” using your slope. rise = 1, run = -3
Repeat this again from your new point.
Draw a line through your points. -3 1 -3 1
Start here

8. Review: Graphing with intercepts: -2x + 3y = 12
Find your x-intercept:
Let y = 0
-2x + 3(0) = 12
x = -6; (-6, 0)
Find your y-intercept:
Let x = 0
-2(0) + 3y = 12
y = 4; (0, 4)
3. Graph both points and draw a line through them.

9. Function - Input-Output Machines
We can think of equations as input-output machines. The x-values being the “inputs” and the y-values being the “outputs.”
Choosing any value for input and plugging it into the equation, we solve for the output.
y = -2x + 5
x = 4
y = -2(4) + 5
y = -3
y =
y = -3

10. Ex: Graph 6x – 3y = 3 Solve for a variable: y x y = 2x - 1 y
y = 2(0) - 1 -1
-6x x 1
y = 2(1) - 1 1
- 3y = 3 – 6x
y = 2(½) - 1
y = x
y = 2x - 1
We have identified 3 solutions to the equation:
(0, -1)
(1, 1)
( ½ , 0)

11. Plotting the three solutions/points we get:
(0, -1)
(1, 1)
( ½ , 0)
The solution points lie on a straight line.
Every point on this line is a solution to the equation 6x – 3y = 3! 1 1

12. Special Cases for Lines:
Special Case 1): Graph 7x + 63 = 0
7x = - 63
x = - 9
x is always – 9  this is a vertical line 3 3 12

13. y is always 4 * this is a  horizontal line
Special Case 2) Graph 12y = 48
12y = 48
y = 4
y is always 4 * this is a  horizontal line 3 3 13

14. Excellent Job !!! Well Done

15. Stop Notes
Do Worksheet