1. Show your work finding all values or y/x using the values in the table.
The quantities are proportional to one another because there is a constant of _____ such that when the number of __________ (x values) is multiplied by the constant, the result is
How to explain that the values in a table are proportional.
1. For each given measure of Quantity "y" and Quantity "x", find the value of "y/x" (y divided by x).
2. If the value of "y/x" (y divided by x) is the same for each pair of numbers, then the quantities are proportional to each other.
Steps to determine if two quantities in a table are proportional to each other:
No, ___________ (?? values) is not proportional to __________ (?? values) because the values of all the ratios of ??/x are not equivalent. There is not a constant where every measure of ?? multiplied by the constant gives the corresponding measure in ??.
How to explain that the values in a table are NOT proportional
The origin is the intersection of the ??-axis and the ??-axis, at the ordered pair (0,0).
What is the origin and where is it located?
The points will appear to be on a line that goes through the origin.
How are proportional quantities represented on a graph?
Yes, it should always be included for proportional relationships. For example, if a worker works zero
hours, then he or she would get paid zero dollars, or if a person drives zero minutes, the distance
covered is zero miles.
Would all proportional relationships pass through the origin?
The graph could go through the origin, but if it does not lie in a straight line, it does not represent two
quantities that are proportional to each other.
what is important to note about graphs of two quantities that are not proportional to each
other?
Both graphs can have points that appear on a line, but the graph of the quantities that are proportional
to each other must also go through the origin.
What are the similarities of the graphs of two quantities that are proportional to each other and the graphs of
two quantities that are not proportional?
Straight line through the origin
How to explain the values in a graph are proportional or not
There are ________ for every ________________.
Explain the meaning of the constant of proportionality in a problem
A constant specifies a unique number.
Constant
A variable is a letter that represents a number.
Variable
Divide to find the unit rate, ??/?? = ??.
How do you find the constant of proportionality?
?? = ??x, substituting the value of the constant of
proportionality in place of ??.
How do you write an equation for a proportional relationship?
?? and ?? values are always left as variables, and when one of them is known, they are substituted into ??=??x to find the unknown using algebra.
What is the structure of proportional relationship equations, and how do we use them?
The points (0,0) and (1, ??), where ?? is the unit rate, are always on the graph.
What points are always on the graph of two quantities that are proportional to each other?
In a table, you can multiply each ??-value by the unit rate to obtain the corresponding ??-value, or you
can divide every ??-value by the unit rate to obtain the corresponding ??-value. You can use the equation
?? = ???? and replace the ?? with the unit r
How can you use the unit rate of ??/?? to create a table, equation, or graph of a relationship of two quantities that are proportional to each other?
From a table, you can divide each ??-value by the corresponding ??-value. If the ratio ?? ? ?? is equivalent
for the entire table, then the value of the ratio, ??/??, is the unit rate, and the relationship is proportional.
In an equation in the form ?? =
How can you identify the unit rate from a table, equation, or graph?