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