Algebra 1: Inequalities
Lesson 9: Graphing Linear Inequalities (Day 2)
Methods for Graphing Equations & Inequalities
Example 1
-2x + 3y > 12
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Algebra 1: Inequalities
Example 2
4x – y ≤ 3
Example 3
3x + y ≥ 0
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Algebra 1: Inequalities
Lesson 9: Graphing Linear Inequalities (Day 2)
1. -2x + y < -2
2. x – 3y ≤ -3
3. 3x – 4y < -8
4. x+y > 3
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Algebra 1: Inequalities
5. 2x + 2y ≤ 6
6. 3x – y ≤ -5
7. 6x – 2y < -12
8. 5x - y > 0
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Algebra 1: Inequalities
Directions: Graph each inequality on the grid. (3 points each)
.
1. 2x - 3y ≥ -12
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2. 5x – y < 3
Algebra 1: Inequalities
Lesson 9: Graphing Linear Inequalities Answer Key
1. -2x + y < -2
X intercept: let y = 0.
Y-intercept: let x = 0
-2x + 0 = -2
-2(0) + y =-2
-2x/-2 = -2/-2
y = -2
x=1
** Substitute (0,0) -2(0) + 0 < -2
0< -2 is not true
3. 3x – 4y < -8
You can either find the x and y intercept or you
can rewrite the equation in slope intercept form.
I rewrote the equation in slope intercept form
because we end up with a fraction for the x
intercept. If you found the intercepts they
would be: x = -8/3 & y = 2
Slope Intercept Form:
Substitute (0,0)
3x -3x – 4y < -3x -8
3x -4y < -8
-4y < -3x – 8
3(0) -4(0) < -8
-4y/-4 < -3x/-4 – 8/-4
0 < -8 is not true.
y > 3/4x + 2
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2. x – 3y ≤ -3
X-intercept: let y = 0
x – 3(0) = -3
x = -3
Y-intercept: let x = 0
0 -3y = -3
-3y/-3 = -3/-3
y=1
**Substitute (0,0): 0 – 3(0) ≤ -3
0 ≤ -3 is not true
4. x+y > 3
You can either find the x and y intercept or you can
rewrite the equation in slope intercept form. I
found it easiest to find the intercepts. If you
rewrote the equation in slope intercept form, the
equation would be: y > -x + 3.
X-intercept: Let y = 0
Y-intercept: let x = 0
X+0 =3
0+y=3
X=3
y=3
Substitute (0,0)
0+0>3
0 > 3 is not true, so shade the side that does not
contain (0,0)
Algebra 1: Inequalities
5. 2x + 2y≤ 6
Easiest method for graphing is to find the x and y
intercepts:
X-intercept: let y = 0 Y-intercept: Let x = 0
2x +2(0) = 6
2(0) + 2y = 6
2x = 6
2y = 6
2x/2 = 6/2
2y/2 = 6/2
x=3
y= 3
Substitute (0,0)
2(0) + 2(0) ≤ 6
0≤ 6 is true, so shade the side that contains
(0,0)
7. 6x – 2y < -12
The easiest method for graphing is to find the x
and y intercepts:
X-intercept: Let y = 0
Y-intercept: let x = 0
6(0) – 2y = -12
6x -2(0) = -12
6x = -12
-2y = -12
6x/6 = -12/6
-2y/-2 = -12/-2
x = -2
y=6
Substitute (0,0)
6(0) – 2(0) < -12
0 < -12 is not true.
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6. 3x – y ≤ -5
If you find the x and y intercepts, you will end up with
a fraction (which you can estimate on your graph).
The x and y intercepts are: x intercept = -5/3 &
y-intercept = 5. Your graph would be more accurate
if you rewrote the equation in slope intercept form:
Slope Intercept Form:
Substitute (0,0)
3x -3x –y ≤ -3x – 5
3(0) – 0 ≤ -5
-y ≤ -3x – 5
0 ≤ -5 is not true, so
-y/-1 ≤ -3x/-1 – 5/-1
shade the side that
Y ≥ 3x + 5
does not contain (0,0).
8. 5x - y > 0
If you found the x and y intercepts, you would find
them both to be 0. You would not be able to
accurately graph your line without knowing another
point. Therefore, the best method is to rewrite in
slope intercept form:
You cannot choose (0,0)
5x -5x - y > -5x + 0
as your ordered pair to
-y > -5x
substitute since it lies on
-y/-1 > -5x/-1
the line. You can choose
y < 5x
any other point not on
the line. I chose (1,1)
5(1) – 1 > 0
4>0 is true
Algebra 1: Inequalities
Directions: Graph each inequality on the grid. (3 points each)
.
1. 2x - 3y ≥ -12
2. 5x – y < 3
This equation is written in standard form, so I
could find the x and y intercepts or rewrite it in
slope intercept form. Since 2 and 3 are both
divisible by 12, I will find the x and y intercepts.
Step 1: This equation can be graphed easiest
by rewriting in slope intercept form.
X intercept:
Y Intercept:
-y < -5x + 3
Let y = 0
Let x = 0
-y/-1 < -5x/-1 +3/-1
2x – 3(0) = -12
2x = -12
2x/2 = -12/2
x= -6
2(0) – 3y = -12
-3y = -12
-3y/-3 = -12/-3
y=4
Y > 5x – 3 for graphing the line: y = 5x-3
(dotted line)
5x-5x – y < 3 – 5x
Step 2: Substitute (0,0) to figure out which half
plane to shade.
Graph the x and y intercept and draw the line.
5(0) – 0 < 3
Step 2: Substitute (0,0)
2(0) – 3(0) ≥ -12
0 ≥ -12 is a true statement, so shade the side
with (0,0).
0<3 is a true statement, so shade the side that
contains (0,0)
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