1. 
Given P = 2l + 2w, solve for w in terms of
P and l.
2. 
Solve for y in terms of x: ½ x – ¼ y = 10
3. 
Given the Area of a parallelogram is
A = bh and the base of the parallelogram
is 3 more than the height, write the Area
of the parallelogram in terms of its base
only.
Algebra II
1
Graphing Linear
Equations and
Inequalities
Algebra II
Linear Equations: Form a line when
graphed...they have a degree of one.
EX:
X+Y=5
Algebra II
3
3 Forms
1. Standard Form Ax + By = C
2. Slope-Intercept Form y = mx + b
3. Point-Slope Form: y – y1 = m(x – x1)
Algebra II
4
Ax + By = C
¡ 
x and y are on the same side of the equal
sign.
¡ 
No Fractions or decimals.
¡ 
A must be positive.
¡ 
To find the slope from standard form:
m = -A/B.
¡ 
To find x intercept, replace y with zero
¡ 
To find y intercept, replace x with zero
Algebra II
5
1. 
4x – 3y = 12
2. 
2x + 5y = 7
3. 
5y = 3x + 20
4. 
3x = 7y + 8
5. 
10 = 2y – 3x
Algebra II
6
1. 2x + 3y = 12
Standard form.
Get the x and y
intercept.
x-int: (6, 0)
y-int: (0, 4)
Algebra II
7
2. 3x – 2y = 4
Standard form.
Get the x and y
intercept.
x-int: (4/3, 0)
y-int: (0, -2)
Algebra II
8
y = mx + b
¡ 
Solved for y
¡ 
m is the slope
¡ 
b is the y intercept à (0, b)
Algebra II
9
1. 
y = 3x + 2
2. 
2y = 5x – 3
3. 
3x + 4y = 12
4. 
-4x = 3y – 7
5. 
3y – x = 10
Algebra II
10
3. y = ¾x – 2
For Slope-Intercept
form, use the
y-intercept and the
slope.
m=¾
b = (0, -2)
Algebra II
11
4. y = -2x + 1
For Slope-Intercept
form, use the
y-intercept and the
slope.
m = -2
b = (0, 1)
Algebra II
12
y – y1 = m(x – x1)
¡ 
m = slope
¡ 
(x1, y1) = point
¡ 
Use the opposite sign for the points!
Algebra II
13
1. 
y – 3 = ½(x + 2)
2. 
y + 2 = -2(x – 1)
3. 
y – 9 = 5(x – 6)
4. 
y + 7 = 2/3(x + 2)
Algebra II
14
5. y-2 = ½(x+4)
For Point-Slope
form, use the
slope and the
given point.
m=½
b = (-4, 2)
Algebra II
15
6. y+1 = -⅔(x-4)
For Point-Slope
form, use the slope
and the given point.
m = -⅔
b = (4, -1)
Algebra II
16
y
The graph of
y=c
is a horizontal
line with
y-intercept (0, c).
x
(0, c)
Algebra II
17
y
7. y = 3
(0, 3)
x
Algebra II
18
y
The graph of
x=c
is a vertical line
with
x-intercept (c, 0).
Algebra II
x
(c, 0)
19
y
8. 
x = -3
(-3, 0)
x
Algebra II
20
¡  Graph
the “boundary line”
**like graphing any other line**
¡  Choose
a test point on one side of the
boundary line
**not on the boundary line**
§  If the test point works, shade that area
§  If the test point does not work, shade the
other area
Algebra II
21
< dotted line
> dotted line
≤ solid line
≥ solid line
Algebra II
22
Graph x < 2
Step 1: Start by
graphing the line x = 2,
with a dotted line
because the symbol is <.
Step 2: Choose a test
point that is not on the
line. (0,0)
0<2
true, so shade that side
of the line.
Algebra II
23
Graph y ≥ 3
Step 1: Start by
graphing the line y = 3,
with a solid line because
the symbol is ≥. (included)
Step 2: Choose a test
point that is not on the
line. (0,0)
0≥3
false, so shade the other
side of the line.
Algebra II
24
Graph x + y < 3
Step 1: Graph x + y = 3,
with a dotted line because
the symbol is <.
x-int: (3, 0)
y-int: (0, 3)
Step 2: Choose a test point
that is not on the line. (0,0)
0+0 < 3
0<3
true, so shade that side of
the line.
Algebra II
25
Graph y > -½x
Step 1: Graph y = -½x, with
a dotted line because the
symbol is >.
m = -½
y-int: (0, 0)
Step 2: Choose a test point
that is not on the line. (0,1)
1 > -½(0)
1>0
true, so shade that side of
the line.
Algebra II
26
Graph y > -3x + 2
Step 1: Graph y = -3x + 2,
with a solid line because the
symbol is >.
m = -3
y-int: (0, 2)
Step 2: Choose a test point
that is not on the line. (0,0)
0 > -3(0) + 2
0>2
false, so shade the other
side of the line.
Algebra II
27
Graph 2x – 3y > 9
Step 1: Graph 2x – 3y = 9,
with a dotted line because
the symbol is >.
x-int: (9/2, 0)
y-int: (0, -3)
Step 2: Choose a test point
that is not on the line. (0,0)
2(0) – 3(0) > 9
0>9
false, so shade the other
side of the line.
Algebra II
28
Antonio loves to go the
movies. He goes both at
night and during the day.
The cost of a matinée is
$6.00. The cost of an
evening show is $8.00. If
Antonio spent $86.00, write
an equation that represents
the number of each type of
movie he attended. Then
graph the model, give the
domain and range, and find
3 combinations that would
satisfy the model.
Algebra II
29
Allen is helping his father collect
all the nails that he dropped in the
garage last week. For his
assistance, his father has promised
to give him a dime for each small
nail and a nickel for each large nail
he finds. If Allen earns $7.90,
write an equation that represents
how many large and small nails he
found. Then graph the model,
give the domain and range, and
find 3 combinations that would
satisfy the model.
Algebra II
30
The equation C = 20h + 50
represents the cost (C) that
a mechanic charges to work
on your car for h number of
hours. Graph this model,
and describe what the y
intercept and slope
represent in this example.
Algebra II
31
The equation C = .25m + 5
represents the cost (C) for a
taxi ride that is m miles
long. Graph this model, and
describe what the y
intercept and slope
represent in this example.
Algebra II
32
Aaron and John are selling Boy
Scout Cookies (a recent invention
to try to compete with the Girl
Scouts). The boys want to earn at
least $208. If Coconut Softies
costs $1.50 per box and Nutty
Bites cost $3.50 per box, write an
inequality to represent how many
boxes of each could sell. Then
graph the model, give the domain
and range, and find 3
combinations that would satisfy
the model.
Algebra II
33