Identifying Proportional Relationships from Graphs
Any proportional relationship on a graph must go through ____ ________.
The origin.
The constant of proportionality has the form ____
from coordinates (x,y).
CP = y/x
Why must the origin be included in any proportional graph?
Because when x is 0 y will ALWAYS be 0 if it is proportional.
True or False:
The unit rate is the same as the CP.
True.
If x is hours and y is tv shows then what does the coordinate (3,10) tell us?
10 tv shows in 3 hours.
True or False:
A curved line on a graph can be proportional.
FALSE
The points (2,6), (4,12), and (6,18) are on a graph. What is the CP?
CP = 3
DOUBLE JEOPARDY: What would the y values be with a CP of 5.5
if x is hours and y is distance, what does the coordinate (3,50) tell us?
50 distance in 3 hours.
Does the coordinate (4,32) share the same CP as the equation 2y=16x?
Yes
DOUBLE JEOPARDY: Make a table with TWO additional sets of quantities that have the same CP.
The equation y=1/2x has a CP of 1/2, what does the reciprocal tell us?
The reciprocal tells us that x=2y.
DOUBLE JEOPARDY: Draw both on a graph in 30 seconds!
Mr. Crespo gets $11 every 2 hours, Ms. Friedlander gets $16 every 3 hours, and Mr. Razin gets $21 every 4 hours.
Who makes the most per hour?
Mr. Crespo
EVERYBODY GETS A CHANCE!
Draw a graph with THREE lines having CP's of 2, 1/2, and 4 in 30 seconds!
Check for work
EVERYBODY GETS A CHANCE!
In 30 seconds, draw and label a graph with the coordinate (2,6) and it corresponds to tutorial class.
Check for correct answer.
Which of the following has the greatest CP:
6y=36x
y=4x
(36,6)
6y=36x has a CP of 6.
The coordinate (5,8) is used for the following scenario:
James does 8 homework assignments in 5 hours.
How many hours does it take for James to do 1 assignment?
It takes James 5/8 hours.
DOUBLE JEOPARDY!
Draw a chart for this scenario, what is the CP?
Give THREE coordinates where the CP is 5 and form an equation from this.
Check for right answer
DOUBLE JEOPARDY: Draw and label a graph where these coordinates may exist in under 30 seconds!
A graph with a STEEP line has a ______ CP.
Give an example of this with 2 lines on a graph.
Large, Big.
If Mr. Crespo pays a maid $215 for 5 hours of work, draw a graph where this would be true AND write an equation for this scenario.
Check for correct answer.
Equation: y=43x
EVERYBODY GETS A CHANCE!
Represent a CP of 4 in THREE different ways that we have learned!
Table, chart, equation
Draw and label a graph with THREE lines of differing CP's and explain how they are different.
(You choose the x and y)
Check for correct answer.