The variable that RESPONDS to the other variable's change.
100
Why do we use tables in mathematics?
Tables help us ORGANIZE our data so we can look for patterns and solve problems.
100
Why do we use graphs in mathematics?
Graphs make it quick and easy to find patterns and to determine if a relationship between two variables are PROPORTIONAL TO each other.
100
Why do we use EQUATIONS in mathematics?
Equations are typically QUICKER and MORE PRECISE in describing and solving relationships than other methods.
100
What is the CONSTANT OF PROPORTIONALITY (k) for the following ordered pairs: (1,2), (2,4), (3,6) (4,8), (5,10) ?
The CONSTANT OF PROPORTIONALITY is y/x = 2/1 = 2.
200
What is the typical variable used to specify the INDEPENDENT variable?
The x variable is typically used, but any variable can be used (besides y).
x = Independent variable
y = Dependent variable
200
Which variable is listed first in a table - the INDEPENDENT variable (x) or the DEPENDENT variable (y)?
The INDEPENDENT variable is always listed first in a table, whether it is a horizontal or vertical table.
200
Which variable is listed along the horizontal (bottom) axis of a graph - the INDEPENDENT variable (x) or the DEPENDENT variable (y)?
The INDEPENDENT variable (x) is always listed along the horizontal (bottom) axis.
200
Which variable is listed alone on one side of the EQUAL SIGN (=); the INDEPENDENT variable (x) or the DEPENDENT variable (y)?
The DEPENDENT variable (y) is listed alone because it is the result of the INDEPENDENT variable (x) being multiplied by the constant (a.k.a.) unit rate (k).
Dependent variable = Rate X Independent variable
200
What is the CONSTANT OF PROPORTIONALITY (k) for the following ordered pairs: (2,1), (4,2), (6,3) (8,4), (10,5) ?
The CONSTANT OF PROPORTIONALITY is y/x = 1/2.
300
Is TIME (like seconds, minutes, hours, days, years, etc.) is always the INDEPENDENT or DEPENDENT variable?
The INDEPENDENT variable because it typically cannot be manipulated or changed.
300
What do we look for in a table, when we are trying to determine if the dependent variable (y) is PROPORTIONAL TO the independent variable (x)?
A CONSTANT OF PROPORTIONALITY (a.k.a. unit rate), which is a number you MULTIPLY the x-values by to get the y-values.
300
What do we look for in a graph, when we are trying to determine if the dependent variable (y) is PROPORTIONAL TO the independent variable (x)?
In a graph of a proportional relationship, the ordered pairs lie on a STRAIGHT, increasing LINE that passes through the ORIGIN (0,0).
300
What does the equation look when the dependent variable (y) is PROPORTIONAL TO the independent variable (x)?
y = kx, where k is a constant number.
300
Is the following set of ordered pairs PROPORTIONAL?
(1,3), (2,6), (3,7), (4,8)
No, there is NOT a Constant of Proportionality.
(1,3) (2,6) (3,7) (4,8)
3/1=3 3/1=3 7/3=2 1/3 8/4=2
400
Is COST always the independent or dependent variable?
COST is always the DEPENDENT variable because it is the result of how much of something you purchase.
400
How do we calculate the CONSTANT OF PROPORTIONALITY (a.k.a. unit rate) from a table of ordered pairs?
The constant (k) is calculated by DIVIDING the dependent variable (y) by the independent variable (x).
k = y / x
400
Where can we find the UNIT RATE (a.k.a. Constant of Proportionality) in a graph?
The UNIT RATE is always the y-value on the straight line where the x-value is 1.
(1,k)
400
Can the equation of a PROPORTIONAL RELATIONSHIP be written as either y=kx or kx=y ?
Yes, the expressions on each side of the equal sign can be switched to the other side without "breaking" the equation.
400
Is the following equation an example of a PROPORTIONAL RELATIONSHIP?
y = 10x
Yes. It takes the form of y=kx, where k=10. This means that you can find the value of the DEPENDENT variable by multiplying the INDEPENDENT variable by 10.
500
Do all PROPORTIONAL RELATIONSHIPS have a specific independent and dependent variable?
No. In some cases, there is not a specific variable that depends upon the other. In cases like this, rely on the order in which the ratio is given.
For example, if we are comparing the # of texts two people send, then there is not truly an independent or dependent variable.
500
Where can we find the UNIT RATE (a.k.a. Constant of Proportionality) in a table?
The UNIT RATE (a.k.a. constant) is the y-value where the x-value = 1.
500
Do graphs of NON-proportional relationships result in a straight, increasing line starting at the Origin (0,0)?
No. Non-proportional relationships may or may NOT start at the Origin (0,0) and are NOT straight, increasing lines.
Note: This is why the graphs in Science are different, because those graphs are not always proportional.
500
Can the equation of a directly PROPORTIONAL RELATIONSHIP include + or - signs, like y=mx+b?
No. The equation of a directly proportional relationship ONLY includes MULTIPLICATION, like y=kx.
500
If the INDEPENDENT variable is the Number of Pencils purchased and the DEPENDENT variable represents the Cost, what does the ordered pair (3,1.50) represent?
(3, 1.50) represents,
"For every 3 pencils it costs $1.50."