Transcript Section 8.2 Equations with Two Variables pages 405

Section 8.2
Equations with Two Variables
pages 405 - 409
In today’s lesson, we will find
solutions of equations with two
variables, such as
y = 3x + 4.
An _______ ____ that makes
such an equation a true
statement is a ________ of
the equation.
Example 1: Finding a Solution
Find the solution of y = 3x + 4
for x = -1.
y = 3x + 4
Replace x with -1.
y = 3(-1) + 4
y = -3 + 4
Multiply.
Add.
y= 1
So, a solution of the equation is
(-1,1)
Why does the last line of the
example say,
“A solution of the equation…”
instead of
“The solution of the equation…?”
Example 2
The equation t = 21 - 0.01n models
the normal low July temperature in
degrees Celsius at Mount Rushmore,
South Dakota. In the equation, t is
the temperature at n meters above
the base of the mountain. Find the
normal low July temperature at
700m above
the base.
Graphing Equations with
Two Variables
An equation with two variables can have
many solutions. One way to show these
solutions is to graph them, which also
gives the graph of the equation. A
______ ________ is any equation
whose graph is a line. The coordinates
of every point on a line in a coordinate
plane make the equation of the line a
true statement.
Graphing a Linear Equation
Graph y = 4x – 2.
• Make a table of values to show
ordered pair solutions.
x
-2
0
2
y = 4x – 2
(x,y)
• Graph the ordered pairs.
Draw a line through the points.
y 8
(-2,-10)
y
5
(0,-2)
6
4
(2,6)
2
-8
-6 -4
-2
x
2
-2
-4
-6
-8
4
6
8
If you use the vertical-line test on
the previous graph, you see that
every x-value has exactly one yvalue.
This means that the relation
y = 4x – 2
is a ________.
A linear equation is a ________
unless its graph is a vertical line.
Graphing a Linear Equation
Graph y = 2x + 1.
• Make a table of values to show
ordered pair solutions.
x
-2
0
2
y = 2x + 1
(x,y)
• Graph the ordered pairs.
Draw a line through the points.
y 8
y
5
(-2,-3)
6
4
(0,1)
-8
(2,5)
x
2
-6 -4
-2
2
-2
-4
-6
-8
4
6
8
Graphing a Linear Equation
Graph y = 1/2 x + 4.
• Make a table of values to show
ordered pair solutions.
x
-2
0
2
y = 1/2 x + 4
(x,y)
• Graph the ordered pairs.
Draw a line through the points.
y 6
y
5
5
(-2,3)
4
3
(0,4)
2
x
1
(2,5)
-4
-3 -2 -1
-1
-2
1
2
3
4