Title: Graphing Lines and Linear Inequalities
1Graphing Lines and Linear Inequalities
Linear Inequalities
Linear Equations
Drive on The Education Highway
2Linear Equations and Graphing 1. Parts of a
Coordinate Plane 2. Slope 3. Slopeintercept Form
of a Linear Equation 4. Graphing by x
yintercepts.
3Parts of a coordinate plane.
4Click on the correct quadrant numbers. Correct
answer applause.
6
5
Quadrant
Quadrant
4
I
II
III
IV
I
II
III
IV
3
2
1
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
Quadrant
Quadrant
2
3
I
II
III
IV
I
II
III
IV
4
5
6
Lesson Start
5Click on the correct axis names. Correct answer
clapping.
6
5
4
3
2
1
xaxis
yaxis
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
2
3
4
5
6
xaxis
yaxis
Lesson Start
6Click on the point for the origin. Correct
answer clapping.
6
5
4
3
2
1
x
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
2
3
4
5
6
y
Lesson Start
7Click on point (3, 5). Correct point
applause.
6
5
4
3
2
1
x
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
2
3
4
5
6
Lesson Start
y
8You chose a line segment instead of a point. Go
back and try again.
INCORRECT ANSWER
9You chose point (5, 3). Each ordered pair is in
the form (x, y)  it follows the alphabet in its
internal order. You find the x value first, then
you find the y value. Where they meet is the
point. Go back and try again.
INCORRECT ANSWER
10Click on the correct ordered pair for the black
point.
6
5
4
3
2
1
x
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
2
5/4
(5, 4)
3
(4, 5)
4/5
4
5
6
Lesson Start
y
11You did not choose an ordered pair. Go back and
try again.
INCORRECT ANSWER
12You chose the ordered pair for the pale green
point. Remember x comes before y in the
alphabet and in an ordered pair. Go back and try
again.
INCORRECT ANSWER
13Return to Main Menu.
Return to Prior Problem.
Continue to Next Lesson.
14Slopes 1. What is a slope? 2. Slope formula 3.
Types of slopes
15What is slope? Slope is the slant of a
line. Slope rise change in ys run change in
xs Slope is a fraction/integer.
Lesson Start
16How to determine the slope when the line goes up.
1. Count the number of units up from the right
point to the left point.
5
4
9
1
2
3
4
5
6
7
8
3
6
2
5
4
1
x
3
7 6 5 4 3 2 1
1 2 3 4 5 6 7
2
2. Put that number on top of the fraction line.
1
Slope 6
1
2
9
3
4
3, Count the number of units to the right.
4. Put that number under the fraction line.
y
Lesson Start
17How to determine the slope when the line goes
down.
1. Count the number of units down from right
point to left point.
5
4
3
1
2
2
1
3
x
4
2. Put that number on top of fraction line.
7 6 5 4 3 2 1
1 2 3 4 5 6 7
5
1
Slope 6
6
2
1
3
2
3
3
4
3. Count the units to the right.
y
4. Put that number under the fraction line.
Lesson Start
18Determine the slope of the line shown.
5
4
3
2
1
x
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
2
3
4
1/3
3/1
y
3/1
1/3
Lesson Start
19The line does not go down. Go back and try again.
INCORRECT ANSWER
Lesson Start
20The line does not rise 3 units, then run 1 unit
to the right. Go back and try again.
INCORRECT ANSWER
Lesson Start
21Determine the slope of the line shown.
5
4
3
2
1
x
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
2
3
4
2/3
3/2
y
3/2
2/3
Lesson Start
22The line does not go up. Go back and try again.
INCORRECT ANSWER
Lesson Start
23The line does not rise 2 units, then run 3 units
to the right. Go back and try again.
INCORRECT ANSWER
Lesson Start
24Slope Formula m (y1  y2)
(x1  x2) where m slope and (x1, y1),
(x2, y2) are points on the line.
Lesson Start
25Example Find the slope for a line with points
(3, 4) and (7, 2) on it.
1. Assign values as follows
(x1, y1) (3, 4) (x2, y2) (7, 2)
2. Substitute them into the formula and solve.
m 4  (2) 6 3
3  7 10 5
Lesson Start
26Find the slope of the line with points (5, 6) and
(2, 9) on it. 1. (x1, y1)
(5, 6)
(2, 9)
Lesson Start
27Find the slope of the line with points (5, 6) and
(2, 9) on it. 1. (x1, y1) (5, 6)
2. (x2, y2)
(5, 6)
(2, 9)
Lesson Start
28Find the slope of the line with points (5, 6) and
(2, 9) on it. 1. (x1, y1) (5, 6)
2. (x2, y2) (2, 9)
6 9 5 2
6  9 5  2
3. m
5  2 6  9
5 2 6 9
Lesson Start
29The slope formula is a case of subtraction on top
and bottom. Go back and try again.
INCORRECT ANSWER
Lesson Start
30You have your xs and ys upside down. Remember
Ys guys are always in the skies! Go back and
try again.
INCORRECT ANSWER
Lesson Start
31You have your xs and ys upside down. You are
also adding when you need to subtract. Go back
and try again.
INCORRECT ANSWER
Lesson Start
32Find the slope of the line with points (5, 6) and
(2, 9) on it. 1. (x1, y1) (5, 6)
2. (x2, y2) (2, 9)
3. m 6  9 3 1
5  2 3
Lesson Start
33Find the slope of the line with points (7, 5) and
(3, 4) on it. m
5  4 1 7  3 4
7  3 4 5  (4) 9
5  (4) 9 3  7 4
5  (4) 9 7  3 4
Lesson Start
34You have your xs and ys upside down. Remember
Ys guys are always in the skies! Go back and
try again.
INCORRECT ANSWER
Lesson Start
35It is not 5  4, it is 5  (4). Go back and try
again.
INCORRECT ANSWER
Lesson Start
36You must start with the y and x from the first
point and end with the y and x from the second
point. Go back and try again.
INCORRECT ANSWER
Lesson Start
37Types of Slopes 1. Positive and Negative
Slopes 2. Special Types of Slopes 3. Determining
Types of Slopes by Looking at Graphs of
Lines 4. Determining Types of Slopes
Algebraically.
Lesson Start
38Positive and Negative Slopes. Type Graph
Algebra
Positive Up left to right. Positive Frac
tion
SMILE
Negative Down left to right.
Negative Fraction
Frown
Lesson Start
392 Special Types of Slopes Type Graphs Algebra
Zero Horizontal Line 0/a, a ? 0
Why, o y, do I look upon the horizon?
Undefined Vertical Line a/0 No Slope
Lesson Start
40Determining Types of Slopes by Looking at
Graphs of Lines
Lesson Start
41Is the slope of the line positive, negative,
zero, or undefined?
5
4
3
2
1
x
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
2
3
4
y

0
?
Lesson Start
42Is the slope of the line positive, negative,
zero, or undefined?
5
4
3
2
1
x
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
2
3
4
y

0
?
Lesson Start
43Is the slope of the line positive, negative,
zero, or undefined?
5
4
3
2
1
x
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
2
3
4
y

0
?
Lesson Start
44Is the slope of the line positive, negative,
zero, or undefined?
5
4
3
2
1
x
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
2
3
4
y

0
?
Lesson Start
45Click on the line with the negative slope.
5
4
3
2
1
x
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
2
3
4
y
Lesson Start
46Click on the line with the zero slope.
5
4
3
2
1
x
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
2
3
4
y
Lesson Start
47Click on the line with the no slope.
5
4
3
2
1
x
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
2
3
4
y
Lesson Start
48Click on the line with the positive slope.
5
4
3
2
1
x
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
2
3
4
y
Lesson Start
49Determining Types of Slopes Algebraically.
Lesson Start
50Is the slope of the line with the 2 points listed
positive, negative, zero, or undefined? Points
(3, 5) and (9, 4)

0
?
Lesson Start
51Is the slope of the line with the 2 points listed
positive, negative, zero, or undefined? Points
(3, 5) and (3, 4)

0
?
Lesson Start
52Is the slope of the line with the 2 points listed
positive, negative, zero, or undefined? Points
(3, 5) and (9, 4)

0
?
Lesson Start
53Is the slope of the line with the 2 points listed
positive, negative, zero, or undefined? Points
(3, 4) and (9, 4)

0
?
Lesson Start
54Return to Main Menu.
Return to Prior Problem.
Continue to Next Lesson.
55Slopeintercept Form of a Linear Equation 1.
Slopeintercept equation 2. Graphing by
slopeintercept 3. Writing slopeintercept
equations
56Slopeintercept Form y mx b where m
slope and b yintercept.
Lesson Start
57Example y 1/2x 4 1/2 m slope 4
b yintercept
Lesson Start
58Graphing by Slopeintercept 1. Graphing lines
with positive/negative slopes. 2. Graphing
lines with zero or undefined/no slopes.
Lesson Start
59The Slopeintercept Song You make the last number
first. Its either up or down. Make the slope in
2 numbers, Or you look like a clown. Top ones
up or down, And the bottoms always right. Youd
better do it well, Or youll get a fright.
(Tune HokeyPokey)
Lesson Start
60Graph y 1/2x 4
4. Draw a line through the 2 points you plotted.
1. Last number is 4, so go up 4 on the yaxis
from the origin and plot a point.
2. Slope is already 2 numbers. Top one is 1, so
go down 1 from the point you just plotted.
5
4
3
3
2
2
1
1
x
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
3. The bottom number is 2, so go 2 units to the
right and plot a point.
2
3
4
y
Lesson Start
61Graph y 2x  3
1
4. Go 1 unit to the right and plot a point.
1. Last number is 3, so go down 3 units from the
origin and plot a point.
2. The slope is only 1 number so put a 1 under
the 2.
5
4
3
2
1
x
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
1
3. Go up 2 from the point you just plotted.
5. Draw a line through the 2 points you plotted.
2
2
3
4
y
Lesson Start
62Click on the graph for y 2/3x  2
5
4
3
2
1
x
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
2
3
4
y
Lesson Start
63The slope is not negative. Go back and try again.
INCORRECT ANSWER
Lesson Start
64You graphed the last number on the xaxis instead
of the yaxis. Go back and try again.
INCORRECT ANSWER
Lesson Start
65Top number is 2, and the bottom is 3, so you do
not go up 3 and over 2. Go back and try again.
INCORRECT ANSWER
Lesson Start
66Click on the graph for y 4x 3
5
4
3
2
1
x
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
2
3
4
y
Lesson Start
67The slope is not positive. Go back and try again.
INCORRECT ANSWER
Lesson Start
68The 4 is not the yintercept, nor is the 3 the
xintercept. Go back and try again.
INCORRECT ANSWER
Lesson Start
69The 4 is the slope, not the xintercept. Go back
and try again.
INCORRECT ANSWER
Lesson Start
70Two Special Graphs Line with a zero
slope And Line with an undefined slope.
Lesson Start
71Line with a zero slope y (no
x) graphs as a horizontal line.
Why, o y, do I look upon the horizon?
Lesson Start
72Graph the equation y 2.
5
4
3
2
1
x
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
2
3
4
y
Lesson Start
73Line with an undefined/no slope x (no
y) graphs as a vertical line.
Lesson Start
74Graph the equation x 4.
5
4
3
2
1
x
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
2
3
4
y
Lesson Start
75Click on the graph for x 3.
5
4
3
2
1
x
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
2
3
4
y
Lesson Start
76You chose the graph for x 3. Go back and try
again.
INCORRECT ANSWER
Lesson Start
77The x (no y) line does not graph as a
horizontal line. Go back and try again.
INCORRECT ANSWER
Lesson Start
78Click on the graph for y 3½.
5
4
3
2
1
x
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
2
3
4
y
Lesson Start
79The y (no x) line does not graph as a
vertical line. Go back and try again.
INCORRECT ANSWER
Lesson Start
80You chose the graph for y 3½. Go back and try
again.
INCORRECT ANSWER
Lesson Start
81Writing Slopeintercept Equations 1. When given
a slope and the yintercept. 2. When given a
slope and one point on the line. 3. When given 2
points on the line.
m ¾, b 1
m ¼, (8, 3)
(3, 7), (5, 12)
Lesson Start
82Writing a slopeintercept equation when given a
slope and the yintercept. Substitute the slope
and the yintercept for the m and b in the
equation. Example m ¾, b 1 y mx b
Slopeint. equation y ¾x  1 The new
equation
Lesson Start
831. Click on the correct equation for a line with
slope 5/3 and yintercept 2.
y 5/3x 2
y 2x 5/3
5/3y 2x
y 5/3x 2
2. Click on the correct slope and
yintercept pair for y 7x  5.
m 7, b 5
m 5, b 7
m 7, b 5
m 1/7, b 5
Lesson Start
84Writing a slopeintercept equation when given a
slope and a point on the line. 1. Substitute the
x, y, and m in the slopeintercept form. 2.
Solve for b. 3. Substitute the slope and the b in
a clean slopeintercept form.
Lesson Start
85Example Write the equation of the line
with slope ¼ and point (8, 3).
y mx b 3 ¼(8) b
1. Substitute the slope, x, and y in the equation.
2. Solve for b.
3 2 b 2 2 5 b
3. Substitute the slope and b in the equation.
y ¼x 5
Lesson Start
861. Click on the correct substitution for a line
with slope 1/3 and point (5, 9).
9 1/3(5) b
5 1/3(9) b
9 1/3x 5
9y 5x 1/3
2. Click on the correct equation for a line with
slope 2/3 and point (6, 4).
y 2/3x
Y 2/3x 4
y 2/3
y 2/3x  6
Lesson Start
87Writing a slopeintercept equation for a line
with 2 points given 1. Find the slope of the
line. 2. Use that slope and the first point
to find the yintercept. 3. Substitute the slope
and the yintercept into the equation.
Lesson Start
88Example Write and equation for a line with
points (3, 7) (5, 12).
m (y1  y2) (x1  x2) m 7  12 5
5 3  5 2 2
1. Find the slope of the line.
Continued on next screen.
Lesson Start
89Write and equation for a line with points (3, 7)
(5, 12). m 5/2 y mx b
7 (5/2)(3) b 2(7) 2(15/2) 2b 14
15 2b 15 15 1 2b ? 1/2 b 2
2
2. Use the slope and the first point to
solve for the yintercept.
Continued on next screen.
Lesson Start
90Write and equation for a line with points (3, 7)
(5, 12). m 5/2, b 1/2
3. Substitute the slope and the yintercept for
the m and the b in the equation.
y mx b y 5/2x  1/2
Lesson Start
911. Click on the slope for a line with
points (2, 8) and (7, 5).
13 9
3 9
9 13
13 9
2. Click on the yintercept for a line
with points (2, 8) and (7, 5).
46 9
86 9
5
86 13
Lesson Start
923. Click on the correct equation for a line with
points (3, 7) and (4, 8).
y 3x 7
y 3/4x 8
y x 4
y x 4
Lesson Start
93Return to Main Menu.
Return to Prior Problem.
Continue to Next Lesson.
94Graphing by x and yintercepts. Xintercept
where the line crosses the xaxis. Yintercept
where the line crosses the yaxis.
xintercept
x
yintercept
y
95How to graph by x yintercepts 1. Cover the x
term with your index finger and solve the
resulting equation for y. 2. Go up or down on the
yaxis from the origin that many units and plot a
point. 3. Cover the y term with your index finger
and solve the resulting equation for x. 4. Go
left or right on the xaxis from the origin that
many units and plot a point. 5. Draw a line
through your points.
Lesson Start
96Graph the line for 3x 2y 6.
1. Cover the x term and solve for y. 3x 2y 6.
2. Go up 3 units on the yaxis.
5. Draw a line through the points plotted.
5
4
3
2
2
y 3
1
1
x
1
7 6 5 4 3 2 1
1 2 3 4 5 6 7
3. Cover the y term and solve for x. 3x 2y 6.
1
4. Go right 2 units on the xaxis.
2
3
4
x 2
y
Lesson Start
971. Click on the correct intercepts for 3x  4y
24.
xint 8 yint 6
xint 8 yint 6
xint 6 yint 8
xint 6 yint 8
Lesson Start
982. Click on the graph of 3x  6y 12.
5
4
3
2
1
x
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
2
3
4
y
Lesson Start
993. Click on the correct equation for the line
shown.
5
9y  6x 36
4
4x 6y 36
3
2
1
x
7 6 5 4 3 2 1
1 2 3 4 5 6 7
1
6y 4x 36
6x  9y 36
2
3
4
y
Lesson Start
100Return to Main Menu.
Return to Prior Problem.
Continue to Next Lesson.
101Graphing Linear Inequalities
Type of Line
Solving Inequalities
Where to Shade
102How to Determine the Type of Line to Draw
103Choose the type of line for the inequality given.
1. y gt 3x  2 a. Solid b. Dotted 2. y gt ¼x 
5 a. Solid b. Dotted
Lesson Start
104Choose the inequality symbol for the line shown.
lt or gt
lt or gt
Lesson Start
105Choose the inequality symbol for the line shown.
lt or gt
lt or gt
Lesson Start
106Where to Shade
For Positive, Negative, Zero Slopes
For Undefined or No Slopes
107Where to Shade for Positive, Negative, and Zero
Slopes
The inequality must be in y ? mx b format.
? can be gt, gt, lt, or lt.
Lesson Start
108Lesson Start
109Graph y gt x  2.
1. Graph the line y x  2.
x
2. Since y gt, shade above the line.
y
Lesson Start
110Graph y lt x  2.
1. Graph the line y x  2.
x
2. Since y lt, shade below the line.
y
Lesson Start
111Do you do anything different when the line is
dotted rather than solid?
Lesson Start
112Not Really
Lesson Start
113Graph y gt x  2.
1. Graph the line y x  2, but make the line
dotted.
x
2. Since y gt, shade above the line.
y
Lesson Start
114Graph y lt x  2.
1. Graph the line y x  2, but make the line
dotted.
x
2. Since y lt, shade below the line.
y
Lesson Start
115Graph y gt ½x 3
Type of line
Solid
Dotted
x
y
Lesson Start
116Graph y gt ½x 3
Type of line
Solid
Dotted
x
Shade ___ the line.
y
Above
Below
Lesson Start
117Graph y gt ½x 3
Type of line
Solid
Dotted
x
Shade ___ the line.
y
Above
Below
Lesson Start
118Choose the correct inequality for the graph
shown.
y lt 1/3 x 2
y lt 1/3 x 2
x
y gt 1/3 x 2
y gt 1/3 x 2
y
Lesson Start
119Where to Shade for Undefined or No Slopes
The inequality must be in x ? (no y) format.
? can be gt, gt, lt, or lt.
Lesson Start
120Lesson Start
121Graph x gt 2
1. Draw a dotted vertical line at x 2.
x
2. Shade to the right of the line.
y
Lesson Start
122Graph x lt 2.
1. Graph the line X 2.
x
2. Shade to the left of the line.
y
Lesson Start
123Graph x gt 3.
Choose type of line.
Solid
Dotted
x
y
Lesson Start
124Graph x gt 3.
Choose type of line.
Solid
x
Choose where to shade.
Left
Right
y
Lesson Start
125Graph x gt 3.
Choose type of line.
Solid
x
Choose where to shade.
Right
y
Lesson Start
126Solving Inequalities You use the same algebraic
methods as solving equations except when you
multiply/divide both sides by the same negative
number. In that case, you switch the direction of
the inequality symbol.
Lesson Start
127Solve 3x  2y lt 12.
3x  2y lt 12
3x 3x
2y lt 3x 12
2 2 2
y lt 3/2 x  6
gt
Lesson Start
128Choose the correct inequality. 1. 2x 5y gt 10
y lt 2/5 x 2
y gt 2/5 x 2
y gt 2/5 x  2
y lt 2/5 x  2
2. 3x  2y gt 10
y lt 2/3 x  5
y gt 2/3 x  5
y gt 2/3 x  5
y lt 2/3 x  5
Lesson Start