The document discusses graphing linear equations using x-y charts. It provides examples of solving single-variable and two-variable linear equations for x and y. Specific examples shown include finding the solution sets for various equations and determining if given points satisfy particular linear equations. Charts are completed and equations are graphed.

1. Objective - To graph linear equations using x-y charts. 1 2 4 5 7 2 2 One Variable Equations Two Variable Equations 2x - 3 = 11 +3 +3 2x = 14 x = 7 One Solution Two Solutions x + y = 5 Solutions: x = 1, y = 4 x = 2, y = 3 x = 4, y = 1 x = 5, y = 0 x = 7, y = -2 Ordered Pairs (x,y) (1,4) (2,3) (4,1) (5,0) (7,-2) x y 4 3 1 0 -2 Infinite Solutions

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) - - 14 = 5 Yes Yes 3(-1) - 2 = 5 No

3. Complete the chart and graph. y = 2x - 3 x y -3 -2 -1 0 1 2 3 2(-3) - 3 = -9 2(-2) - 3 = -7 -5 -3 -1 1 3 x y

4. Complete the chart and graph. y = 2x - 3 x y -3 -2 -1 0 1 2 3 2(-3) - 3 = -9 2(-2) - 3 = -7 -5 -3 -1 1 3 x y

5. Complete the chart and graph. y = 2x - 3 x y -3 -2 -1 0 1 2 3 2(-3) - 3 = -9 2(-2) - 3 = -7 -5 -3 -1 1 3 x y

6. Complete the chart and graph. y = 2x - 3 x y -3 -2 -1 0 1 2 3 2(-3) - 3 = -9 2(-2) - 3 = -7 -5 -3 -1 1 3 x y

7. Complete the chart and graph. y = 2x - 3 x y -3 -2 -1 0 1 2 3 2(-3) - 3 = -9 2(-2) - 3 = -7 -5 -3 -1 1 3 x y

8. Complete the chart and graph. y = 2x - 3 x y -3 -2 -1 0 1 2 3 2(-3) - 3 = -9 2(-2) - 3 = -7 -5 -3 -1 1 3 This line represents all real solutions to y = 2x - 3. x y

9. 1) 2x + y = 5 2) - x + 2y = - 4 - 2x - 2x y = - 2x + 5 + x + x 2y = x - 4 2 2 Solve the following equations for y. (Function Form)

10. 3) 3x + 5y = 10 4) - 2x + 3y = - 6 - 3x - 3x 5y = - 3x + 10 5 5 + 2x + 2x Rewrite the equation in function form. 3y = 2x - 6 3 3

11. Solve the equation for y, complete the chart, and graph. 1) 3x + 2y = 4 - 3x - 3x 2y = - 3x + 4 2 2 x y -4 -2 0 2 4 6 8 5 2 -1 -4 -7 x y

12. Rewrite in function form, complete the chart, and graph. 2) x - 3y = 6 - x - x -3y = - x + 6 - 3 - 3 x y -6 -3 0 3 6 9 -4 -3 -2 -1 0 1 x y

13. Solve the equation for y, find at least five solutions, and graph. 3) x + 2y = 8 - x - x 2y = - x + 8 2 2 x y -4 -2 0 2 4 6 6 5 4 3 2 1 x y