Transcript File

Dr. Fowler  CCM
Graphing Linear Equations
 Point slope
 x & y intercepts
 Pick 3 points
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.
3x  4 y  11 is linear.
Parts of a Coordinate Plane
QUADRANT II
QUADRANT I
(-x, y)
(x, y)
Origin
QUADRANT III
(-x, -y)
QUADRANT IV
(x, -y)
Y-Axis
X-Axis
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
(0,-4)
Examples: (0,-4)
(6, 0)
(-3,-6)
(-3, -6)
Slope-Intercept Form
y = mx + b
m = slope
b = y-intercept
Graph using slope & y-intercept
Standard Form
ax + by = c
Graph using
x & y intercepts
Graphing with slope-intercept
1. Start by graphing the
y-intercept (b = 2).
2. From the y-intercept,
apply “rise over run”
using your slope. 
1
rise = 1, run = -3  m   3 
3. Repeat this again
from your new
point.
4. Draw a line through
your points.
1
y
x2
3
-3
1
-3
1
Start here
Review: Graphing with intercepts:
1. Find your x-intercept:
-2x + 3y = 12
Let y = 0
-2x + 3(0) = 12
x = -6; (-6, 0)
2. 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.
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.
x=4
y = -2x + 5
y = -2(4) + 5
y = -8 + 5
y = -3
y = -3
Ex: Graph 6x – 3y = 3
Solve for a variable: y
6x – 3y = 3
-6x
-6x
- 3y = 3 – 6x
-3
-3
y = - 1 + 2x
y = 2x - 1
x
y = 2x - 1
y
0
y = 2(0) - 1
-1
1
y = 2(1) - 1
1
½
y = 2(½) - 1 0
We have identified 3 solutions to the equation:
(0, -1)
(1, 1)
( ½ , 0)
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
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
Special Case 2) Graph 12y = 48
12y = 48
y=4
y is always 4 * this is a  horizontal line
3
3
Excellent Job !!!
Well Done
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