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Chapter 4 – Graphing Linear Equations and Functions
Algebra I A - Meeting 22
Section 4.1 – Plot Points in a Coordinate Plane
Coordinate Plane – a plane formed by the intersection, also known as the origin, of a
horizontal number line called the x-axis and a vertical number line called the y-axis.
Quadrants – The four regions into which the coordinate plane is divided by the x-axis
and the y-axis.
Ordered Pair – a pair of numbers, the x-coordinate and y-coordinate, that can be used to
locate a point on a coordinate plane. (x-coordinate, y-coordinate)
Coordinate Plane
Chapter 4 – Graphing Linear Equations and Functions
Algebra I A - Meeting 22
Section 4.1 – Plot Points in a Coordinate Plane
Example # 1
Using the Overhead, plot the points on the coordinate plane. Describe the location of
each point.
a)
b)
c)
d)
e)
f)
g)
h)
2,3
5,2
3,0
3,2
0,3
5,3
7,5
 6,2
 2,3
j) 3,2
k) 0,3
l) 1,5
m) 6,5
n) 0,0
o) 7,0
p) 0,6
i)
 2,3
r)  5,3
s) 1,3
t)  7,6
u) 0,6
v) 5,5
w)  4,3
x) 2,1
q)
y)
2,3
z)  1,1
aa) 4,5
ab) 1,6
ac) 6,1
ad) 5,0
a)  1,7
af)  5,5
Chapter 4 – Graphing Linear Equations and Functions
Algebra I A - Meeting 22
Section 4.1 – Plot Points in a Coordinate Plane
Example # 2
1
Graph the function y   x  1
2
with the domain -4, -2, 0, 2, 4. Identify the range.
Step 3: Graph the Function, use the
ordered pairs
Step 1: Make a Input-Output Table:
y = -(1/2)x +1
y
-4
y = -(1/2)(-4) +1
3
-2
y = -(1/2)(-2) +1
2
0
y = -(1/2)(0) +1
1
2
y = -(1/2)(2) +1
0
4
y = -(1/2)(4) +1
-1
Step 2: List the Ordered Pairs:
 4,3
 2,2
0,1
2,0
4,1
y = -(1/2)x +1
4
(-4, 3)
y-values
x
-5
3
(-2, 2)
2
1
(0, 1)
(2, 0)
0
-4
-3
-2
-1-1 0
1
-2
x-values
Step 4: Identify the range. -1, 0, 1, 2, 3.
2
3
4
(4, -1)
5
Chapter 4 – Graphing Linear Equations and Functions
Algebra I A - Meeting 22
Section 4.2 – Graph Linear Equations
Example # 3
Graph the equation 2x + y = 2
Step 1 : Solve the given equation in terms of y.
Step 4 : Connect the points by drawing a line with
arrows at both ends.
2 x  y  2  y  2 x  2
Step 2 : Make a Input-Output Table:
y = -2x+2
-3
y =-2(-3)+2
8
-1
y =-2(-1)+2
4
0
y =-2(0)+2
2
1
y =-2(1)+2
0
3
y =-2(3)+2
2x + y = 2
Y
-4
Step 3 : List & Plot the Ordered
Pairs(Points)
 3,8  1,4 0,2 1,0 3,4
10
(-3, 8)
y-values
x
-4
5
(-1, 4)
(0, 2)
(1, 0)
0
-3
-2
-1
0
-5
x-values
1
2
3
(3, -4)
4
Chapter 4 – Graphing Linear Equations and Functions
Algebra I A - Meeting 22
Section 4.2 – Graph Linear Equations
Standard Form of a Linear Equation – Ax + By = C
where A, B, and C, are all real numbers
A and B are not both zero.
If either A or B is zero, then you have special types of lines.
When A = 0, the equation becomes By = C or y = (C/B).
Thus, y equals a constant value, or y = b.
And that constant value forms a horizontal line.
When B = 0, the equation becomes Ax = C or x = (C/A).
Thus, x equals a constant value, or x = a.
And that constant value forms a vertical line.
HORIZONTAL AND VERTICAL LINES
y=b
x=a
In the coordinate plane,
In the coordinate plane,
the graph y = b is a horizontal line.
the graph x = a is a horizontal line.
Chapter 4 – Graphing Linear Equations and Functions
Algebra I A - Meeting 22
Section 4.2 – Graph Linear Equations
Example # 4
Graph the equation y = -3
For every value of x, the value of y is -3. The graph of the equation, y = -3 is a horizontal
line 3 units below the x-axis.
y = -3
y-values
0
-1
-2
-3
-4
(-3, -3)
(0, -3)
x-values
(2, 3)
Chapter 4 – Graphing Linear Equations and Functions
Algebra I A - Meeting 22
Section 4.2 – Graph Linear Equations
Example # 5
Graph the equation x = 2
For every value of y, the value of x is 2. The graph of the equation, x = 2, is a vertical line
2 units to the right of the y-axis.
y-values
x=2
4
3
2
1
0
-1
-2
(2, 3)
(2, 0)
(2, -1)
x-values
Chapter 4 – Graphing Linear Equations and Functions
Algebra I A - Meeting 22
Section 4.2 – Graph Linear Equations
Example # 6
1
Graph the function y  x  1 with the domain x ≤ 0. Identify the range of the function.
2
Step 3: Graph the Function, use the
ordered pairs
Step 1: Make a Input-Output Table:
Reminder: x must be less than 0
y = (1/2)x -1
0
y = (1/2)(0) -1
-1
-2
y = (1/2)(-2) -1
-2
-4
y = (1/2)(-4) -1
-3
-6
y = (1/2)(-6) -1
-4
-8
y = (1/2)(-8) -1
-5
Step 2: List the Ordered Pairs:
0,1
 2,2
 4,3
 6,4
 8,5
y = (1/2)x -1
y
-9 -8 -7 -6 -5 -4 -3 -2 -1
0
1
(0, -1)
y-values
x
(-2, -2)
(-4, -3)
(-6, -4)
(-8, -5)
x-values
Step 4: Identify the range. y ≤ -1.
2
0
-1
-2
-3
-4
-5
-6
Chapter 4 – Graphing Linear Equations and Functions
Algebra I A - Meeting 22
Section 4.2 – Graph Linear Equations
Practice Problem
Graph the function y  3 x  1 with the domain x ≤ 0. Identify the range of the function.
y = -3x + 1
12
10
8
6
4
2
0
y-values
(-3, 10)
(-2, 7)
(-1, 4)
(0, 1)
-4
-3
-2
-1
x-values
Identify the range.
y ≥1
0
1
2
Chapter 4 – Graphing Linear Equations and Functions
Section 4.1, 4.2
Homework # 15
pg 209 # 3 – 21 odd; # 36
pg 219 # 3 – 21 mults. of 3; # 23 -29 all
Algebra I A - Meeting 22