Independent and Dependent Variables

​This equation shows how the number of dolls made by Judy depends on the number of weeks she has spent making them.

l = 4n

The variable n represents the number of weeks Judy has spent making dolls.

The variable l represents the total number of dolls. After 5 weeks, how many dolls does Judy make in total?

​12p = w

The above equation shows the total number of games Andre has, depending on the money he spent on additional games.

The variable w represents the money he spent on games and the variable p represents the total number of games.

If he spent $60 on games, how many games did he get?

​

​​Depends on the value of some other number

• ​It is a value that is being changed

• ​The dependent variable is the OUTPUT value

• ​Represented by the variable, y

​Dependent Variable

​​A variable that represents a quantity that is being manipulated and influences the other

• ​​The Independent variable is the INPUT value

• ​Represented by the variable, x

• ​Example: any category with time like minutes, hours, days, weeks...is independent

Independant

​X-Axis (Input Value)

​Y-Axis (Output Value)

​Many real-world situations involve TWO Variable quantities.

One quantity depends on the other.

​The quantity that depends on the other is called the dependent variable, and the quantity it depends on is called the independent variable.

• ​Kory bought Some shirts that cost $20 each. How much did he Spend?

• The amount he spent depended on the number of shirts he purchased.

​1 shirt, spent $20

2 shirts, spent $40

3 shirts, spent $60

​Independent Means does not need help.

Dependent means does need help.

​Weeks	​Money Saved
​0	​15
​1	​20
​2	​25
​3	​30

​I Identify which variable independent(x) 1st column

​I Identify which variable dependent(y)

2nd column

​1 shirt, spent $20

2 shirts, spent $40

3 shirts, spent $60

​We can make a table of the Independent, the number of shirts, and the dependent, amount he spent

​We don't know how much he spent until we know how many shirts he bought.

we don't know y until we know x

​y = 20 x

​y depends x

​amount spent

​Number of Shirts

​Cost per Shirt

x	Shirts	​0	1​	​2	​3	​4
y	​Amount	​0	​20	​40	​60	​80

​y = 20 x is an equation in two variables in which the value of y is dependent on the value of x.

• ​This equation represents the relationship between the amount of money spent and the number of shirts purchased.

• The value of y is always 20 times the value of x.

• This relationship is based on multiplication so it's a multiplicative relationship.

​We can use this equation in two Variables to determine any amount spent.

​y = 20 x

​number of shirts	​amount spent

​( x , y )

​( 10 , 200 )

​( x , 300 )

• ​A car is moving at a constant speed on a highway the distance y in miles that the car has traveled after x hours is shown in the table.

x	Time​	​0	​1	​2	​3	​4
y	​Miles	​0	​60	​120	​180	​240

​y = 60x Equation

y depends on x

• ​We don't know the distance until we know the time.

• We don't know y until we know x.

​y = 60 x

​Total =

Distance

(rate)

Time in hours driving

• ​y = 60x is an equation in two variables in which the value of y is dependent on the value of x.

• This equation represents the relationship between the distance traveled in miles and the

• The value of y is always 60 times the value of x.

• The relationship is based on multiplication, so it's a multiplicative relationship.

​x	​0	​1	​	​3	​	​
y​	​	​20	​	​60	​	​

​The value of y is 20 times the value of x.

• ​Sam bought some shirts that cost $ 20 each

• How Much did he spend?

• The amount spend depends on the number of shirts he bought.

• ​The graph shows the relationship between the two variables.

• If sam buys 5 shirts, he will spend $ 100.

​Amount Spent

​Number of Shirts

​