Download Graphing inequalities Lesson 14

Graphing inequalities
Lesson 14
Warm Ups Lesson 14
At both Quick Car Rental and Speedy Car Rental, the cost, in dollars, of
renting a full size car depends on a fixed daily rental fee and a fixed charge
per mile that the car is driven. However, the daily rental fee and the charge
per mile are not the same for the 2 companies. In the graph below, line Q
represents the total cost for quick car rental and line S represents the total
cost for speedy car rental
$60
Q
$50
S
1. Robert plans to rent a full-size car for 1
day and drive 50 miles. Which company
will be cheaper, and how much will he
save?
2. If y rent a full size car from quick car
rental for 1 day, how much more would the
total rental cost be if you drove the car 78
miles than if you drove it 77 miles?
$40
$30
$20
3. What would be the total cost of renting a
full size car from Speedy Car Rental for 1
day and driving the car 150 miles?
$10
0
0
20
40
60
80 100 miles
Putting inequality in slope intercept form
Solve the following
inequality for y
Move everything
except y over to the
right.
Get rid of the
coefficient of y
(multiply or divide)
2x - 2y + 6 > 4
3x - 6y + 6 > 12
-2x
- 6 -6 – 2x -3x
- 6 -6 - 3x
-2y
> -2 – 2x
-6y > 6 – 3x
-2y
-2
y
-6y > 6 – 3x
> -2 – 2x
-2
-6y > 6 – 3x
<1 + x
-6
y
-6
<-1 + ½ x
Solve like a 2 variable equations except when you multiply or divide
by a negative.
Solve the following inequalities
1. 2x + 4y < 16
y<-½x+4
3. 4x – 5y ≤ -15
y ≥ 4/ 5 x + 3
5. 2x + 4y > - 6
y > - 1/ 2 x – 3/ 2
2. 3y – 6x > -9
y > 2x - 3
4. 2(2x -3y) ≥ 12
y ≤ 2/ 3 x - 2
6. 3y -2(x + 4) < -15
y < 2/ 3 x – 7/ 3
Graphing inequalities
Graph the following equation
-4x + 2y < 2
1. Solve for y
y
2y < 4x + 2
•
y<2x+1
2. Determine m (slope)
of the equation and b
(y-intercept
•
m=2
b=1
x
•
3. Graph the y
intercept.
4. Using the
slope fine 2
more points.
5. Draw a line through
the points. Use a
dashed line if the
inequality is < or >.
6. Fill in the side of the line
that makes the equation true.
Graphing inequalities
Graph the following equation
1. Solve for y
y≤x+2
2. Determine m (slope)
of the equation and b
(y-intercept
3. Graph the y
intercept.
y≤x+2
y
m=1
•
b=2
•
•
Try (1,1)
x
y≤x+2
1≤1+2
1 ≤ 3 which is true
4. Using the
slope fine 2
more points.
5. Draw a line through
the points. Use a
dashed line if the
inequality is < or >.
6. Fill in the side of the line
that makes the equation true.
Solving system of inequalities
y < 5/4x – 2
2(x + y) ≥ 5
1. Solve for y on 1st
equation
y < 5/4x - 2
2. Determine m (slope)
of the equation and b
(y-intercept
3. Graph the y
intercept.
y
m = 5/4
•
b = -2
Try (1,1)
x
y < 5/4x - 2
1≤
5/
4
•
-2
1 ≤ -3/4 which is false
4. Using the
slope fine 2
more points.
5. Draw a line through
the points. Use a
dashed line if the
inequality is < or >.
•6.
Fill in the side of the line
that makes the equation true.
Graphing inequalities
7. Solve for y 2nd
equation
2(x + y) ≥ 5
2x + 2y ≥ 5
2y ≥ -2x + 5
8. Determine m (slope)
of the equation and b
(y-intercept
m = -1
b = 5/2
9. Graph the y
intercept.
y
y ≥- x + 5/2
•
•
•
Try (1,1)
x
2(x + y) ≥ 5
2(1 + 1) ≥ 5
2(2) ≥ 5
4 ≥ 5 which is false
10. Using the
slope fine 2
more points.
11. Draw a line
through the points.
Use a dashed line if
the inequality is < or >.
12. Fill in the side of the line
that makes the equation true.
Homework
Lesson 14