1. Bell Work: Multiply. Write the answer in descending order of the variable. (3x + 2) 2

2. Answer: 9x + 12x + 4 2

3. Lesson 51: Graphs of Linear Equations, Graphs of Vertical and Horizontal Lines

4. If we use a rectangular coordinate system to graph the ordered pairs that satisfy a first-degree polynomial equation in two variables, we find that the graph is the graph of a straight line. For this reason, we call a first- degree polynomial equation in one or more variables a linear equation.

5. The following equations are examples of linear equations in two variables. y – 2x + 1 = 0 x – 4 = -2y x + y = 0

6. To graph a linear equation in two variables, we need to know only two ordered pairs of x and y that satisfy the equation since only two points are needed to determine the graph of a line. But since the topic is a new one, in the examples we will learn how to find two or more ordered pairs of x and y that lie on the line.

7. Example: Graph y = 2x – 1

8. Answer: xy 0 23 -2-5 35 -3-7

9. Practice: Graph y = -1/2 x + 2

10. Answer: xy 02 21 -23

11. Practice: Graph y = -x

12. Answer: xy 00 3-3 3

13. In the previous problems we note that each of equation has both an x term and a y term. We also note that none of the graphs was a vertical line or a horizontal line.

14. Some equations of a straight line contain either an x term or a y term but not both, and the graph of these equations is either a vertical line or a horizontal line.

15. The graph of every vertical line on the coordinate plane has the form x = h, where h is the value of the x coordinate of any point on the vertical line. Note that h can be a positive number, a negative number, or zero.

16. The graph of every horizontal line on the coordinate plane has the form y = k, where k is the value of the y coordinate of any point on the horizontal line. Note that k can be a positive number, a negative number, or zero.

17. Practice: Graph x = -2

18. Answer:

19. Practice: Graph y = 4

20. Answer:

21. Practice: Graph y = 2x and y = 2 on the same rectangular coordinate system.

22. Answer:

23. HW: Lesson 51 #1-30