1. Graphing Linear Equations by Picking Points

2. Let’s look at some examples . . .
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 . . .

3. Graph: y = 2x + 3
First, we will construct a table of values. x y

4. Pick values for the complicated side – the one with all the action!
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!

5. Pick 3 easy x’s x y 1 -1
Pick numbers near zero so that they’ll fit on your graph!

6. Find the corresponding y’s
y = 2x + 3 x y 3 1 5 -1
‘cause
3 = 2 ( 0 ) + 3
5 = 2 ( 1 ) + 3
1 = 2 ( -1 ) + 3
Our points are ( 0, 3 ), ( 1, 5 ), ( -1, 1 )

7. Connect: ( 0, 3 ), ( 1, 5 ), ( -1, 1 ) (1, 5) This is the graph of
y = 2x + 3
This is the graph of
(0, 3)
( 0, 3 )
( -1, 1 )

8. Graph: 3y – 2 = x
First, we will construct a table of values. x y

9. Pick values for the complicated side – the one with all the action!
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!

10. Pick 3 easy y’s y x 1 -1
Pick numbers near zero so that they’ll fit on your graph!

11. Find the corresponding x’s
Graph: 3y – 2 = x x y -2 1 -5 -1
‘cause
3 ( 0 ) - 2 = -2
3 ( 1 ) - 2 = 1
3 ( -1 ) - 2 = -5
Our points are ( -2, 0 ), ( 1, 1 ), ( -5, -1 )

12. Connect: ( -2, 0 ), ( 1, 1 ), ( -5, -1 ) This is the graph of
3y – 2 = x
This is the graph of
(1, 1)
(-2, 0)
(-5, -1)

13. 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:
Add -2x to each side
Divide by 3

14. Pick values for the complicated side – the one with all the action!
Graph:
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!

15. Pick one x that makes y an integer
5/3 1
Nope
Hooray!
Since the denominator is 3, you may have to try 3 consecutive numbers to find a winner.

16. Find your other 2 x’s 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 = and 1 – 3 = - 2

17. Try x = 4
( 4, -1 ) works!

18. Try x = -2
( -2, 3 ) works!

19. This is a table of the values we’ve foundx y 1 4 -1 -2 3
Our points are ( 1, 1 ), ( 4, -1 ), ( -2, 3 )

20. Connect: ( 1, 1 ), ( 4, -1 ), ( -2, 3 ) (1, 5) This is the graph of
( 1, 5 )
This is the graph of
This is the graph of
2x + 3y = 5
(-2,3)
(0, 3)
( 0, 3 )
(1, 1)
( -1, 1 )
(4,-1)

21. 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!