1. Objective - To graph linear equations using x-y charts.
3:2 Graphing Linear Equations Using X-Y Charts
Lesson 3.2 Graphing Linear Equations Using X-Y Charts
Objective - To graph linear equations using x-y charts.
One Variable Equations
Two Variable Equations
2x - 3 = 11
x + y = 5
Ordered
Pairs (x,y) x y
2x = 14
Solutions: 1 2 4 5 7 4 3 1 -2
x = 1, y = 4
(1,4)
x = 7
x = 2, y = 3
(2,3)
x = 4, y = 1
(4,1)
One Solution
x = 5, y = 0
(5,0)
x = 7, y = -2
(7,-2)
Two Solutions
Infinite Solutions
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
Algebra 1 by James Wenk © 2003 published by TEACHINGpoint

2. State whether the given point is a solution to 3x - y = 5. 1) (2, 1)
2) (4, 5)
3) (-3, -14) 4)
5) (-1, 2)
3(2) - 1 = 5
Yes
3(4) - 5 = 5 No
3(-3) = 5
Yes
Yes
3(-1) - 2 = 5 No
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

3. Complete the chart and graph.y
y = 2x - 3 x y -3 -2 -1 1 2 3
2(-3) - 3
= -9
2(-2) - 3
= -7 -5 x -3 -1 1 3
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

4. Complete the chart and graph.y
y = 2x - 3 x y -3 -2 -1 1 2 3
2(-3) - 3
= -9
2(-2) - 3
= -7 -5 x -3 -1 1 3
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

5. Complete the chart and graph.y
y = 2x - 3 x y -3 -2 -1 1 2 3
2(-3) - 3
= -9
2(-2) - 3
= -7 -5 x -3 -1 1 3
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

6. Complete the chart and graph.y
y = 2x - 3 x y -3 -2 -1 1 2 3
2(-3) - 3
= -9
2(-2) - 3
= -7 -5 x -3 -1 1 3
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

7. Complete the chart and graph.y
y = 2x - 3 x y -3 -2 -1 1 2 3
2(-3) - 3
= -9
2(-2) - 3
= -7 -5 x -3 -1 1 3
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

8. Complete the chart and graph.y
y = 2x - 3 x y -3 -2 -1 1 2 3
2(-3) - 3
= -9
2(-2) - 3
= -7 -5 x -3 -1 1 3
This line represents all
real solutions to y = 2x - 3.
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

9. Solve the following equations for y. 1) 2x + y = 5 2) -x + 2y = -4
-2x x
+x x
2y = x - 4
y = -2x + 5
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

10. Solve the following equations for y. 3) 3x + 5y = 10 4) -2x + 3y = -6
-3x x
+2x x
5y = -3x + 10
3y = 2x - 6
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

11. Solve the equation for y, complete the chart, and graph.
1) 3x + 2y = 4
-3x x y x y
2y = -3x + 4 -4 -2 2 4 6 8 5 2 x -1 -4 -7
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

12. Solve the equation for y, complete the chart, and graph.
2) x - 3y = 6
-x x y x y
-3y = -x + 6 -6 -3 3 6 9 -4 -3 -2 x -1 1
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

13. Solve the equation for y, find at least five solutions, and graph.
3) x + 2y = 8 y
-x x x y
2y = -x + 8 -4 -2 2 4 6 6 5 4 x 3 2 1
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series