bell work: multiply. write the answer in descending order of the variable. (3x + 2) 2

Bell Work:

Multiply. Write the answer in descending order of the variable.

(3x + 2)2

Answer:

9x + 12x + 42

Lesson 51: Graphs of Linear

Equations, Graphs of Vertical and Horizontal

Lines

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.

The following equations are examples of linear equations in two variables.

y – 2x + 1 = 0

x – 4 = -2y

x + y = 0

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.

Example:

Graph y = 2x – 1

Answer: x y

0 -1

2 3

-2 -5

3 5

-3 -7

Practice:

Graph y = -1/2 x + 2

Answer:x y

0 2

2 1

-2 3

Practice:

Graph y = -x

Answer:x y

0 0

3 -3

-3 3

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.

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.

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.

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.

Practice:

Graph x = -2

Answer:

Practice:

Graph y = 4

Answer:

Practice:

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

Answer:

HW: Lesson 51 #1-30