Transcript Graphing Linear Equations

Graphing Linear
Equations
What is a Linear Equation?
y
A linear equation is an equation
whose graph is a LINE.
x
Linear
Not Linear
What is a Linear Equation?
y
The equations we will be graphing
have two variables, x and y.
For example:
2x+ 3y = 12
A solution to the equation is any
ordered pair (x , y) that makes this
equation true.
The ordered pair (3 , 2) is a
solution since…
2(3)+ 3(2)= 12
If we were to plot all these ordered
pairs on a graph, we would be
graphing a line.
x
2(0)+ 3(4)= 12
2(- 3)+ 3(6)= 12
2(6)+ 3(0)= 12
2(- 1)+ 3 4 2 = 12
3
( )
Graphing a Linear Equation
y
How do we graph linear equations?
Let’s try: y = 3x – 2
Make a table (or T-chart)
x
x
y
–2
–8
–1
0
–5
–2
1
1
2
4
yComplete
= 3(–2) –the
2 = –8
by inputting
ytable
= 3(–1)
– 2 = –5
the x - values and
y = 3(0) – 2 = –2
calculating the
y = 3(1) – 2 =y1corresponding
values.
y = 3(2) – 2 = 4
You get to pick the x - values!
Graphing a Linear Equation
y
Now let’s try x – 2y = 5.
First Step:
Write y as a function of x:
x – 2y = 5
–2y = – x + 5
y  1 x 5
2 2
x
Graphing a Linear Equation
y
Let’s continue with x – 2y = 5
Second Step:
Make a table
x
–2
–1
0
1
x
y
7
2
–3

5
2
–2
y  1 x 5
2 2
Let’s
complete
the chart…
Find INTERCEPT points for a graph to
help with graphing:
To find the x-intercept: set y =0 (x,0)
 To find the y-intercept: set x = 0 (0,y)

Graphing Horizontal & Vertical Lines
y
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 …
x
Graph x = 3
Since there are no y – values in
this equation, x is always 3 and y
can be any other real number.
y = –2
Graph y = –2
Since there are no x – values in
this equation, y is always – 2 and
x can be any other real number.
x=3
Midpoint formula:
The midpoint formula can be
thought of as
(avg of x values, avg of y
values),
or
 x1  x2 y1  y2  .
,


2 
 2
…So we
average the x
and y values to
get the
midpoint.
The
midpoint is
half-way
between the
two points…