Download 8.2 - Mathmatuch

Homework
Text p. 388, #8-22 evens and #19
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8) domain: -2, -1, 0, 1;
range: -9, 2, 4, 5
10) domain: -4, -3, 2, 4;
range: -1, 0
12) sometimes
14) function
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16) relation, -10 has 2
outputs
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18) no
19) yes
20) no
22) a). yes, the graph
passes the vertical line test
b). advisories 20-30
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Do Now 1/31/12

Be ready for
The POTD!
Take out HW from Monday.
– Text p. 388, #8-22 evens and #19

Copy HW in your planner.
– Text p. 394, #12-23 all (8 graphs)
Each input must be paired with only
 In your notebook,
telloutput
whether each table
ONE
is aafunction
function or notNotaafunction.
Not
function
Function
x 0 2 4 4 8
y 4 3 2 1 0
x 1 1 2 3 5
y 4 3 2 1 0
x 1 2 3 4 5
y 3 3 6 8 10
Objective

SWBAT find solutions of equations in two
variables
Section 8.2 “Linear Equations in
Two Variables”
An example of an equation in two
variables is 2x – y = 5. The solution of
an equation in two variables, x and y, is an
ordered pair (x, y) that produces a true
statement when substituted into the
equation.
Solving Linear Equations

To find a SOLUTION, substitute the
ordered pair into the equation and see if it
produces a true statement.
2x – y = 5
Tell whether the ordered pair is a solution to the equation.
NO
YES
ordered pair
equation
(1, 3)
2x - y = 5
2(1) – 3 = 5
2x - y = 5
2(2) – -1 = 5
(2,-1)
substitution
check
-1 = 5
5=5
Linear Equationan equation whose graph is a line
y = 4 – 2x
Graph an Equation
Graph the equation
y = 4 – 2x.
y  4  2x
x
-2
y-axis
(-2,8)
y
6
0
4
1
2
2
0
8
(-1,6)
8
-1
10
6
4
(0,4)
(1,2)
2
-12 -10 -8
x-axis
-6 -4 -2
0
2
-2
-4
-6
Is this a function?
Yes, it passes the
vertical line test
-8
-10
4
(2,0)
6
8
10 12
Graph an Equation
Graph the equation
y = 3x - 4
y-axis
10
y  3x  4
x
y
-2
-10
-1
-7
0
-4
1
-1
2
2
8
6
4
2
-12 -10 -8
-6 -4 -2
x-axis
0
(2,2)
2
4
-2(1,-1)
(0,-4)
-4
-6
(-1,-7)
-8
-10
(-2,-10)
6
8
10 12
Graph an Equation
Graph the equation
y = 2.
HORIZONTAL LINE
y=b
STEP 2
STEP 1
Solve the equation for y.
STEP 3
Make a table by
choosing a few values
for x and then finding
values for y.
y2
x
-2 -1
0
1
2
y
2
2
2
2
2
Plot the points. Notice
the points appear on a
line. Connect the points
drawing a line through
them.
Graph an Equation
Graph the equation
x = -1.
VERTICAL LINE
STEP 2
STEP 1
Solve the equation for x.
STEP 3
Make a table by
choosing a few values
for x and then finding
values for y.
1 x  0 y  1
x  1
x=a
Plot the points. Notice
the points appear on a
line. Connect the points
drawing a line through
them.
x
-1 -1 -1 -1 -1
y
-2 -1
0
1
2
Homework
Text p. 394, #12-23 all