graphing linear equations from the beginning. what is a linear equation? a linear equation is an...
TRANSCRIPT
Graphing Linear Equations
From the beginning
What is a Linear Equation?
A linear equation is an equation whose graph is a LINE.
y
x
Linear
Not Linear
( ) ( )2 3 3 2 12+ =
What is a Linear Equation?
A solution to the equation is any ordered pair (x, y) that makes the equation true.
If we were to plot all these ordered pairs on a graph, we would be graphing a line.
The equations we will be graphing have two variables, x and y.
2 3 12x y+ =
y
x
For example,
The ordered pair (3 , 2) is a solution since,
( ) ( )2 0 3 4 12+ =
( ) ( )2 6 3 0 12+ =
( ) ( )2 3 3 6 12- + =
( ) ( )22 1 3 4 123
- + =
The x - values are picked by YOU!
Complete the table by inputting the x - values and calculating the corresponding y - values.
Graphing a Linear Equationy
x
How do we graph linear equations?
Let’s try this one: y = 3x – 2
Make a Table of values
x y
–2
–1
0
1
2
y = 3(–2) – 2
y = –8
y = 3(–1) – 2
y = –5
y = 3(0) – 2
y= –2
y = 3(2) – 2
y= 4
y = 3(1) – 2
y= 1
–8
–5
–2
1
4
Graphing a Linear Equationy
x
How about another one!
Let’s try y = 5-2x.
First Step:
Make a Table of Values
8
1
Take a moment and complete the chart…
9
5
3
x y
–2
–1
0
1
2
Graphing Horizontal & Vertical Linesy
x
When you are asked to graph a line, and there is only ONE variable in the equation, the line will either be vertical or horizontal. For example …
Graph x = 3
Since there are no y – values in this equation, x is always 3 and y can be
any other real number.
x = 3
Graph y = –2
Since there are no x – values in this equation, y is always – 2 and x can
be any other real number.
y = –2