Transcript General School Presentation

Graphing Linear Equations
by
Picking Points
Picking 3 points
Given the equation of a line, we know that an ordered pair
is on the line if we can substitute its values for the x and y
in the equation and get a true statement.
To graph a line from an equation, we typically find 3 such
points and connect the dots.
Let’s look at some examples . . .
Graph:
y = 2x + 3
First, we will construct a table of values.
x
y
Graph:
y = 2x + 3
Pick values for the complicated side – the one with all the action!
• In this example, pick 3 values for x.
•If you pick an ‘x’ that makes ‘y’ a fraction, pick again!
Pick 3 easy x’s
x
0
1
-1
y
Pick numbers near zero so that they’ll fit on your graph!
Find the corresponding y’s
y = 2x + 3
x
0
1
-1
y
3
5
1
‘cause
3=2(0)+3
5=2(1)+3
1 = 2 ( -1 ) + 3
Our points are ( 0, 3 ), ( 1, 5 ), ( -1, 1 )
Connect:
( 0, 3 ), ( 1, 5 ), ( -1, 1 )
( (1,
1, 5 5)
)
( (0,
0, 3 3)
)
This is the
graph of
y = 2x + 3
( -1, 1 )
Graph:
3y – 2 = x
First, we will construct a table of values.
x
y
Graph: 3y – 2 = x
Pick values for the complicated side – the one with all the action!
• In this example, pick 3 values for y.
•If you pick a ‘y’ that makes ‘x’ a fraction, pick again!
Pick 3 easy y’s
y
0
1
-1
x
Pick numbers near zero so that they’ll fit on your graph!
Find the corresponding x’s
Graph: 3y – 2 = x
x
-2
1
-5
y
0
1
-1
‘cause
3 ( 0 ) - 2 = -2
3(1)-2=1
3 ( -1 ) - 2 = -5
Our points are ( -2, 0 ), ( 1, 1 ), ( -5, -1 )
Connect:
( -2, 0 ), ( 1, 1 ), ( -5, -1 )
(1, 1)
(-2, 0)
(-5, -1)
This is the
graph of
3y – 2 = x
Graph:
2x + 3y = 5
It is easier to order to construct a table of values, if the
equation is solved for either x or y.
This equation can be transformed:
2x + 3y = 5
3y = -2x+5
-2
5
y=
x
3
3
Add -2x to each side
Divide by 3
Graph:
-2
5
y= x 
3
3
Pick values for the complicated side – the one with all the action!
• In this example, pick 3 values for x.
•If you pick an ‘x’ that makes ‘y’ a fraction, pick again!
Pick one x that makes y an integer
-2
5
y= x 
3
3
x
y
0
5/3
1
1
Nope
Hooray!
Since the denominator is 3, you may have to try 3 consecutive
numbers to find a winner.
Find your other 2 x’s
-2
5
y= x 
3
3
We know that x = 1 gave us a “good” value for y.
Since 3 is the denominator, we can get other “good” x values
by adding + 3 or - 3 to x = 1.
Let’s try
1+3=4
and 1 – 3 = - 2
Try x = 4
2
5
y
x
3
3
2 4 5
y

3 1 3
8 5
y

3 3
3
y
3
y  1
( 4, -1 ) works!
Try x = -2
2
5
y
x
3
3
2 2 5
y

3 1 3
4 5
y 
3 3
9
y
3
y3
( -2, 3 ) works!
This is a table of the values we’ve found
x
y
1
4
-2
1
-1
3
Our points are ( 1, 1 ), ( 4, -1 ), ( -2, 3 )
Connect: ( 1, 1 ), ( 4, -1 ), ( -2, 3 )
( (1,
1, 5 5)
)
(-2,3)
( (0,
0, 3 3)
)
(1, 1)
( -1, 1 )
(4,-1)
This is the
graph of
2x + 3y = 5
When asked to graph the equation of a line
by plotting points:
• Solve for either x or y
• Pick 3 values for the letter that’s on
the “complicated” side.
• Calculate the corresponding value
for the other letter. Skip numbers
that give you fractions.
• Plot the points
• Connect the dots!