3 2 Graphing Linear Equations Using XY Charts

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

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

Complete the chart and graph. y = 2 x - 3 y x y -3 -2 -1 0 1 2 3 2(-3) - 3 = -9 2(-2) - 3 = -7 -5 -3 -1 1 3 x 3 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Complete the chart and graph. y = 2 x - 3 y x y -3 -2 -1 0 1 2 3 2(-3) - 3 = -9 2(-2) - 3 = -7 -5 -3 -1 1 3 x 4 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Complete the chart and graph. y = 2 x - 3 y x y -3 -2 -1 0 1 2 3 2(-3) - 3 = -9 2(-2) - 3 = -7 -5 -3 -1 1 3 x 5 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Complete the chart and graph. y = 2 x - 3 y x y -3 -2 -1 0 1 2 3 2(-3) - 3 = -9 2(-2) - 3 = -7 -5 -3 -1 1 3 x 6 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Complete the chart and graph. y = 2 x - 3 y x y -3 -2 -1 0 1 2 3 2(-3) - 3 = -9 2(-2) - 3 = -7 -5 -3 -1 1 3 x 7 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Complete the chart and graph. y = 2 x - 3 y x y -3 -2 -1 0 1 2 3 2(-3) - 3 = -9 2(-2) - 3 = -7 -5 -3 -1 1 3 x This line represents all real solutions to y = 2 x - 3. 8 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

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

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

Solve the equation for y, complete the chart, and graph. 1) 3 x + 2 y = 4 -3 x 2 y = -3 x + 4 2 2 x y -4 8 -2 5 0 2 y x 2 -1 4 -4 6 -7 11 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Solve the equation for y, complete the chart, and graph. 2) x - 3 y = 6 -x -x -3 y = -x + 6 -3 -3 x y y -6 -4 -3 -3 0 -2 x 3 -1 6 0 9 1 12 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Solve the equation for y, find at least five solutions, and graph. 3) x + 2 y = 8 y -x -x x y 2 y = -x + 8 -4 6 2 2 -2 5 0 4 2 3 4 2 6 1 x 13 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series