Direct & Partial Variation
Slope
Rate of Change
First Differences
Rule of Four
100
Identify each as either direct or partial variation, or neither.
a)y=x+3 b)y=x^2+1 c)y=5x^2
a) Partial
b) Neither
c) Neither
100
Find the slope of the hill
m=6/11
100
True or False?
The rate of change is the slope
True
100
What do you use first difference for?
To determine whether a line is linear or not.
100
What are the four ways to represent a relation?
Table
Graph
Equation
Description
200
What is the constant of variation?
3.33
200
Find the slope of the line
m=5/2
200
What makes rate of change different from slope?
Rate of change has a unit at the end of it.
200
List 3 steps to on how to find the first difference
Step 1: Subtract the second term with the first term
Step 2: Subtract the third term with the second term
Step 3: Decide if the relation is linear or not
200
The cost to enter a park is $30, plus $5 per ticket. Write an equation for this relationship.
C=5t+30
300
Identify the initial value and constant of variation
Initial Value: -2
Constant of Variation:
1/3
300
State the lines in order from greatest to least magnitude.
Green
Red
Blue
300
A teenager's heart pumps an average of 7200 L of blood every 24 h. What is the rate of change of volume of blood?
300 L/h
300
What is the first difference of this relation?
First Difference=3
300
Write a description for the relation given.
The runner starts at home. Every second he runs 5 km further from his home.
400
Does this table of values represent a direct or partial variation?
Partial Variation
400
Find the slope of
(1/2,3) and (3/4,1/2)
m=-10
400
Find the rate of change from the table. Interpret its meaning.
Rate of Change= 2.5 dollars/year
This means that the average cost of a car per year is $2.50.
400
Is the relation linear? Partial or Direct?
Linear and Partial
400
The cost to install a heater is $100, plus $5/h.
Write an equation for this relationship.
If you were charged $350, how much time was spent on the installation?
C=5h+100
50 hours were spent on the installation
500
A school is planning an awards banquet. The cost of renting the banquet and hiring staff is $675. There is an additional cost of $12 per person for the meal.
a) Initial value and Constant of Variation
b) Form an equation to represent this relationship
a) IV: 675 CV: 12
b) c=12p+675
500
A roof has to be 20 m high to meet safety regulations. If the width of the roof is 10 m and the slope is 8/5 m. Does the height meet safety regulations?
No because the height of the roof is 16 m.
500
Calculate the rate of change of from the graph. Write an equation for the relationship.
Rate of Change= -3.6 m/s
s=-3.6t+18
500
How can you determine if a relation is linear from its equation?
If the degree of the equation is one, then the relation is linear.
ex.
y=x+3
500
Form an equation based off of the graph. How long will it take to travel 80 km.
d=15h
It will take 5.33 hours.