Relationships
The velocity of a car
versus
The time it takes to travel to the destination
Is it a direct or inverse relationship?
inverse relationship
What is always true about a direct proportion graph?
1. the line passes through the point (0,0) (the origin)
2. the line is straight
Given the points (1,3) and (4,¾ ). Is their relationship direct or inverse? What is the value of x in (x,6)? What is the equation relating y and x?
inverse relationship
½
y=3/x
Given the points (2,½ ) and (½ ,2). Is their relationship direct or inverse? What is the value of y in (3,y)? What is the equation relating y and x?
inverse relationship
⅓
y=1/x
x y
8 3
4 1.5
2 ?
0.75 or 3/4
The price of mandarins
versus
The quantity of mandarins bought
Is it a direct or inverse relationship?
direct relationship
What is always true about an inverse proportion graph?
1. The line can never pass through the point (0,0) (the origin)
2. The line is curved
Given the points (2,1) and (4,2). Is their relationship direct or inverse? What is the value of x in (x,7)? What is the equation relating y and x?
direct relationship
14
y=½ x
Given the points (5,8) and (10,16). Is their relationship direct or inverse? What is the value of y in (3,y)? What is the equation relating y and x?
direct relationship
24/5
y=8/5 x
x y
10 1/2
15 1/3
? 1/4
20
The number of people working on a project
versus
The time it takes them to complete the project
Is it a direct or inverse relationship?
inverse relationship
Describe how you can find the constant of proportionality from a direct proportion graph.
Choose a point on the graph and divide the y by the x
Given the points (4,1.5) and (2,3). Is their relationship direct or inverse? What is the value of y in (3,y)? What is the equation relating y and x?
inverse relationship
2
y=6/x
Given the points (2,4) and (4,2). Is their relationship direct or inverse? What is the value of x in (x,1)? What is the equation relating y and x?
inverse relationship
8
y=8/x
x y
6 2
24 ?
15 5
8
The level of gasoline in a car
versus
The distance that it can travel
Is it a direct or inverse relationship?
direct relationship
Describe how you can find the constant of proportionality from an indirect proportion graph.
Square the x (or y) coordinate of the “knee” point
Given the points (5,15/4) and (3,9/4). Is their relationship direct or inverse? What is the value of x in (x,1)? What is the equation relating y and x?
direct relationship
4/3
y=¾ x
Given the points (8,48/7) and (7, 6). Is their relationship direct or inverse? What is the value of y in (2,y)? What is the equation relating y and x?
direct relationship
12/7
y=6/7 x
x y
1 9
9 1
5 ?
9/5
What is the name of the yellow animal that lives in Zane's hometown?
Banana Slug
x y
1/3 27/17
? 1/17
2 9/34
9
x y
6 42
? 70
9 63
10
x y
7 1/3
3 ?
5 7/15
7/9
x y
3 24
4 32
? 48
6