straight line

parabola

half-plane

half of a parabola

( -1, 2)

(- 1, 3)

( -2, 3)

(-2, 4)

0

1

2

infinite

Linear equations are mathematical statements with no solutions while linear inequalities are mathematical statements with solutions.

Linear equations are mathematical statements with equal sign while linear inequalities are mathematical statements with inequality sign.

Linear equations are mathematical statements that cannot be graphed while linear inequalities are mathematical statements that can be graphed.

Linear equations are mathematical statements with more than 2 variables while linear inequalities are mathematical statements with only one variable.

   g ≤ 75                        

g = 75           

g ≥ 75     

none of these

domain              

function               

range  

relation

domain

function

range 

relation

$$3x+2y\ge140$$

$$3x+2y\le140$$

$$3x+2y>140$$

$$3x+2y<140$$

 {(1,2), (2,4), (5,9), (2,3)}

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

{(1,2), (2,3), (3,4), (3,5)}

{(1,1), (2,1), (2,3), (3,5)}

The variable y is the dependent variable because its value depends on the value of x. 

The variable y is considered the independent variable because any value could be assigned to it.

Dependent variable is a mathematical variable whose value is determined by that of one or more other variables in a function.

Independent variable is a mathematical variable that is independent on the other variables in an expression or function and whose value determines one or more of the values of the other variables.

Number of liters of water wasted

Number of minutes the water runs

The minutes the water runs and liters of water wasted.

No independent variable.

set of all x values

set of all first values

set of all independent values

All of the above

{0,1,2,3}

{0,1,2, -4}

{1,-3,2, -4}

{1,-3, -4}

{0,1,2,3}

{1,2,3,4}

{2,3,4,5}

{1,2,2,3,3,4,4,5}

{x|x ∈ ℜ} , {y|y ∈ ℜ} 

{x|x > 0} , {y|y < 0}

{x|x > 1} , {y|y >-1}

{x|x ≥ -2} , {y|y ≥ 2}

Php12,000

Php1,200

Php120

Php600

f(x) = 51.68x        

f(x) = x+51.68  

f(x) = x/51.68  

f(x) = x-51.68

Jimmy goes on vacation

to Orlando he will go

he will go to Orlando

goes on vacation

If p, then q.

If q, then p.

If not p, then not q.

If not q, then not p.

If a student is loved by his teacher, then he is honest

If a student is honest, then he is loved by his teachers

If a student is not loved by his teacher, then he is not honest

If a student is not honest, then he is not loved by his teachers

By recycling bottles, can and paper, you will help save the environment.

If you recycle bottles, can and paper, then you will help save the environment.

If you want to save the environment, then you must recycle bottles, can, and paper.

Students like you must know how to recycle bottles, can and paper to help save the environment.

A square is a shape with four sides.

If a shape is a square, then the shape has four sides.

If a shape has four sides, then the shape is a square.

If a shape is not a square, then the shape has four sides.

the angle is an acute angle

the angle is not an acute angle

the measure of the angle is above 90°

the measure of the angle is below 90°

If you are in love, you are not inspired.

If you are inspired, then you are in love.

If you are not inspired, then you are not in love.

If you are not in love, then you are not inspired.

If the number is divisible by 2 and 3, then it is divisible by 6.

If the number is divisible by 6, then it is divisible by 2 and 3.

If the number is not divisible by 2 and 3, then it is not divisible by 6.

If the number is not divisible by 6, then it is not divisible by 2 and 3.

11

12

13

14

If an angle is acute, then its measure is not between 0 to 90 degrees.

If an angle is not acute, then its measure is not between 0 to 90 degrees

If an angle measures between 0 to 90 degrees, then it is acute angle.

If an angle is not acute, then its measure is between 0 to 90 degrees

If p, then q.

If q, then p.

If not p, then not q.

If not q, then not p.

If p, then q.

If q, then p.

If not p, then not q.

If not q, then not p.

q p

p q

p q

p

Deductive Reasoning

Indirect Proof

Direct Proof

Inductive Reasoning

conductive

deductive

inductive

interactive

using logic to draw conclusions based on accepted statements

accepting the meaning of a term without definition

defining mathematical terms in relation with physical objects

inferring a general truth by examining a number of specific examples

Deductive Reasoning

Indirect Proof

Direct Proof

Inductive Reasoning

∠B and ∠C are congruent angles.

∠B and ∠C have equal measures.

∠B and ∠C are right angles.

∠B and ∠C are not congruent.

If a shape is a rectangle, then it is a parallelogram.

If a shape is a parallelogram, then it is a rectangle.

If a shape is not a rectangle, then it is not a parallelogram.

If a shape is not a parallelogram, then it is not a rectangle.