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

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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?