WARM UP OCT. 1ST Come in, get a tracking sheet from the basket, and

quietly begin the warm up.1. Write the ordered pair that describes a point 4 units

down from and 3 units to the right of the origin.

2. Write the ordered pair that is 8 units to the left of the origin and lies on the x-axis.

For #3-6, identify the quadrant for each ordered pair.3. ( -1 , 7 ) 4. ( 9 , 2 )

5. ( 0.75 , -4 ) 6. ( 0 , 5 )

7. Which property makes the following true? 3(x – 5) = 3x – 15

HOMEWORK ANSWERS – 4.1

HOMEWORK ANSWERS (CONT.) – 4.1

HOMEWORK ANSWERS – 4.3

HOMEWORK ANSWERS (CONT.) – 4.3

EQUATIONS AS RELATIONS The equation y = 3x + 4 is an example of an equation in

two variables because it contains x and y.

A solution of an equation in 2 variables is an ordered pair. Only a certain set of ordered pairs work for this equation and make it true. What does it mean if an equation is true? It means that both sides

have the same number!

A REPLACEMENT SET is a set of ordered pairs that could replace x and y. We have to pick the ones that work!

A SOLUTION SET is a set of ordered pairs that work for the relation.

SOLVE USING A REPLACEMENT SET1. Find the solution set for -3 = 2x – y , given the

replacement set {(-2, -1), (-1, 3), (0, 4), (3, 9)}.Make a table. Substitute the x and y-values of each ordered pair into the equation.

Solution SetX Y -3 = 2x – y True or False?

HOW ABOUT THIS ONE?2. Find the solution set, given the replacement set

3x + 2y = 6 {(2, 3), (0, 1), (0, 3), (2, 0)}

Solution Set:

X Y 3x + 2y = 6 True or False?

CAN YOU GET THIS ONE ON YOUR OWN?3. Solve 2x – 3y = 5 given the replacement set

{(0, 0), (1, -1), (4, 1), (-2, 3)}

REMEMBER DOMAIN AND RANGE FROM FRIDAY?

Domain = x Range = y

Sometimes, we are given a domain for an equation and we need to find out the range.

Note: Domain is also known as INPUT, and Range is also known as OUTPUT.

WHEN WE ARE GIVEN DOMAIN AND ASKED TO FIND RANGE:

Step 1: Solve the equation for y if necessary. (We want to know our y-values so we need to get

it by itself!) Step 2: Create a table and fill it in! Step 3: Write your ordered pairs as a solution

set.

SOLVE USING A GIVEN DOMAINExample: Solve 1 = 2x – y if the domain is {-2, -1, 0, 2,

4}.

Solution Set:

x y (x, y)

HOW ABOUT THIS ONE?Find the solution set, given the domain.

4x + 8 = 2y x = {-4, -2, 0, 2, 4}.

Solution Set: {(-4, ), (-2, ), (0, ), (2, ), (4, )}

YOU TRY!3. Solve y – 2 = x given the domain {-2, -1, 0, 1,

2}.

BUT WAIT…ON FRIDAY, WE SAID THAT THERE WERE 4 WAYS TO SHOW A RELATION

What were they again? Ordered pairs Table Graph Mapping

Graphs are the easiest way to visually represent a relation, so let’s practice graphing our solution sets.

SOLVE AND GRAPH THE SOLUTION1. Solve 4x + 2y = 12 if the domain is (-1, 0, 2, 4}.

Graph the solution set.

HOW ABOUT THIS ONE?Solve y – 3x = -2 given the domain {-2, -1, 0,

1, 2}. Graph the solution set.

YOU TRY!1. Solve 2y = x + 2 given the domain {-4, -2, 0,

2, 4}. Graph the solution set.

NOW THAT WE KNOW WHAT WE’RE DOING, LET’S LEARN ANOTHER WAY TO FIND SOLUTIONS TO SOME OF THESE EQUATIONS…

USING OUR CALCULATOR!

WITH OUR CALCULATOR!Find the solution set, given the replacement set

4x + 2y = 8 {(2, 3), (0, 1), (0, 3), (2, 0)}

Solve for y.

Calculator Steps:

1.

2.

3.

4.

Solution Set:

WITH OUR CALCULATOR!2. Find the solution set, given the domain.

6x + 2 = 2y x = {-4, -2, 0, 2, 4}.

Solve for y.

Calculator Steps:

1.

2.

3.

4.

Solution Set: {(-4, ), (-2, ), (0, ), (2, ), (4, )}

WITH OUR CALCULATOR!Solve y – 4x = -5 given the domain {-2, -1, 0,

1, 2}. Graph the solution set.Solve for y.

Calculator Steps:

1.

2.

3.

4.

5.

HOMEWORKColossal Creature Worksheet

EXIT QUIZComplete on a half sheet of notebook paper. Be sure

to PUT YOUR NAME AT THE TOP SO I CAN GIVE YOU CREDIT!

1. Write the solution set to the equation y = 2x + 3 if the domain is {-2, 0, 3}

2. Which of the following ordered pairs satisfy the equation y = 5 – 6x? Write them as a solution set.{(1, -1), (4, -3), (-1, 11), (-3, 23), (0, 15)}

3. Solve and graph the solution set to the following equation 6x – 3y = 9 given the domain { -2, -1, 0, 1, 2}

VOCABULARY SHEET Throughout the year, we are learning many

important math vocabulary words. It’s almost like learning a new language. These words are important for your:

Tests Midterm Final End of Course Test ENTIRE MATH CAREER!

So, to make sure we know them, I am giving you a handy-dandy vocabulary sheet to keep in the front of your binder at all times.

Each unit, we will add new words to it.

LET’S GO BACK AND ADD SOME OLD WORDS

Brainstorm: What should we add?