EQUATIONS IN TWO VARIABLES
Unit 3, Lesson 5November 19th, 2014
February 17, 2015
DO NOW (3 MINS)PRIOR KNOWLEDGE BOX (PKB)
Topic: Equations in two variable Misconceptions
Write about what you know about the topic above.
STANDARDSA-CED.2: Create equations that describe numbers or relationships.
• Create equations and inequalities in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
A-REI.10 Represent and solve equations and inequalities graphically.
• Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
OBJECTIVE• Huskies will be able to
• define the solutions of a linear equation in two variables
• Use various techniques to graph a linear equation in two variables
• Find the solutions to a linear equation in two variables using substitution and graphing
• Huskies will show success of the criteria above by earning a 3 out of 4 on the exit slip today
VOCABULARY• Standard Form- An equation of a line that has the
following formula Ax + By = C, where A≠0 and
B≠0.
Examples of Standard Form Equations Non-Examples
3x + 5y = 3 2y = 4x + 2
2x - y = 6 x = 6 - y
-2x + y = 7 y = 2x + 7
LINEAR EQUATIONS IN TWO VARIABLES
Identify the equations that are not linear equations in two variables, and explain why.
Equationx + y = 1
y = 32x2 + y =25
x + y = 2x +y -1
m + n = 1x + y = z
1x+ 1y= 0
y = 12x + 2
The graph of a linear equation in two variablesline. To be a linear equation it must be a first degree equation.
Discuss:
x + 2y = 7
What different methods could you use to graph this equation? How would you determine where the line intersected the x- and y-axes?
THE GRAPH OF LINEAR EQUATIONS
FINDING SOLUTIONSGiven a value for one of the variables, you can find a solution to the equation by solving for the other variable.
1. What is the solution to the equation 2x + y = 9 when x = 0.5?
2. What is the solution to the equation 2x +y = 9 when y = 0.5
3. Find three more solutions to the equation 2x +y = 9
Graph the equation. Find the x-intercept. Find the y-intercept. What is the slope of the line?
Graph 2y - x = 7Graph y = -2x - 3Graph 2x + y = 9 What is the slope of 2x + y = 9
& 2y - x = 7
1. Describe each line
What can we say about theslope of parallel and perpendicular lines?
YOU TRY For each of the following equations, determine where the graph intersects the x- and y-axes and then create a graph.
a. 2x = y +4
b. y =1 -x
c. 2x+2y +5 = 0
YOU TRY 1
Graph 2x = y +4
x-intercept:y-intercept:
Don’t forget: x-intercept (x, 0) y-intercept (0,y)
YOU TRY 2
Graph y = 1 - x
x-intercept:y-intercept:
Don’t forget: x-intercept (x, 0) y-intercept (0,y)
YOU TRY 3
Graph 2x + 2y +5=0
x-intercept:y-intercept:
Don’t forget: x-intercept (x, 0) y-intercept (0,y)
LINEAR EQUATIONS IN TWO VARIABLES
Read and Discuss the handout (elbow partners).
Refer to the the different graphs above
GUIDED PRACTICE PAGE 9
• Dos Variable Equations Cafe Menu
Make sure that you fill your knowledge tank up by completing as much as you can!
• Appetizers
• Entree
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Your reward today = working towards a stamp!!
PRIOR KNOWLEDGE BOX (PKB)
Topic: Equations in two variable Misconceptions
What did you think you knew but you found out was a
misconception? If you didn’t have any prior knowledge, what did you learn/review
today?