| Vocabulary | C.O.P based on Tables | C.O.P. based on Graphs | Random Proportion Questions | Write an Equation |
| 100 | 100 | 100 | 100 | 100 |
| 200 | 200 | 200 | 200 | 200 |
| 300 | 300 | 300 | 300 | 300 |
| 400 | 400 | 400 | 400 | 400 |
| 500 | 500 | 500 | 500 | 500 |
| Final Question | ||||
A special rate where the denominator is 1 is called ____________
A special rate where the denominator is 1 is called ____________
A unit rate.
A comparison between the ratio of two quantities is called ______________
A comparison between the ratio of two quantities is called ______________
The constant of proportionality.
When two quantities have the same ratio, these are said to be ______________ to each other.
When two quantities have the same ratio, these are said to be ______________ to each other.
proportional
The formula to find the constant of proportionality is __________
The formula to find the constant of proportionality is __________
y=kx
y and x are proportional values and k is the constant of proportionality.
what is a constant?
what is a constant?
a value that NEVER changes.
Does this represent a proportion?
Does this represent a proportion?
No, there is no constant of prop.
|
X |
5 | 6 | 7 | 8 |
|
Y |
15 | 18 | 21 | 24 |
|
X |
5 | 6 | 7 | 8 |
|
Y |
15 | 18 | 21 | 24 |
Yes, the constant is 3.
|
Amount of Candy (pounds) |
2 |
3 |
5 |
|
Cost (Dollars) |
5 |
8 |
17 |
Is the relationship proportional? If so, what is the constant?
|
Amount of Candy (pounds) |
2 |
3 |
5 |
|
Cost (Dollars) |
5 |
8 |
17 |
Is the relationship proportional? If so, what is the constant?
No, there is no constant of proportionality.
Does this represent a proportional relationship? If so, what is the constant of prop?
Does this represent a proportional relationship? If so, what is the constant of prop?
Yes, the COP is 4.
Does this represent a proportion? If so, what is the constant of prop?
Does this represent a proportion? If so, what is the constant of prop?
Yes, the COP is 1/2 or .5
Which graph represents a proportional relationship?
Which graph represents a proportional relationship?
Graph B is a straight line and hits the origin!
What is the constant of proportionality?
What is the constant of proportionality?
The COP is 2.
What is the constant of proportionality based on the graph? (hint: it is NOT 3)
What is the constant of proportionality based on the graph? (hint: it is NOT 3)
The constant is 1/3.
What is the constant of proportionality in this graph?
What is the constant of proportionality in this graph?
The COP is 9.
Why is the constant of proportionality 7 in this graph?
Why is the constant of proportionality 7 in this graph?
Because the constant of proportionality is a constant ratio between two proportional relationships. The constant ratio in this graph is 7, each set of x and y values are multiplied by 7.
The graph below represents how many miles someone runs compared to the time it takes. What does the point (0,0) represent in terms of this graph?
The graph below represents how many miles someone runs compared to the time it takes. What does the point (0,0) represent in terms of this graph?
When the person runs for 0 minutes, they haven't ran any distance at all.
How many miles would this person run after 8 minutes?
How many miles would this person run after 8 minutes?
The y value is 40. This person would've ran 40 miles after 8 minutes.
How many web visits could we expect with 1 download?
How many web visits could we expect with 1 download?
When there were 4 downloads, 12 people visited, so;
12 visits / 4 downloads = 3 visits / 1 download.
Three people visited when there was 1 download.
If Mr.McDonald makes 12 baskets in game 1, 15 baskets in game 2, and 18 baskets in game 3. Is the number of games played proportional to the number of baskets Mr. McDonald makes?
If Mr.McDonald makes 12 baskets in game 1, 15 baskets in game 2, and 18 baskets in game 3. Is the number of games played proportional to the number of baskets Mr. McDonald makes?
No,
| games | # of baskets |
| 1 | 12 |
| 2 | 15 |
| 3 | 18 |
There is no constant of proportionality in this relationship.
If a boy posts 3 pictures on Instagram on one day to the 6 pictures a girl posts on the same day, is the relationship between the boys' posts and the girls' posts proportional?
If a boy posts 3 pictures on Instagram on one day to the 6 pictures a girl posts on the same day, is the relationship between the boys' posts and the girls' posts proportional?
Yes, the constant of proportionality is 2. In other words, for every picture a boy posts, a girl posts 2 pictures during one day.
| boy | girl |
| 3 | 6 |
| 4 | 8 |
| 5 | 10 |
Write the formula for this relationship in the form of y = kx.
Write the formula for this relationship in the form of y = kx.
y = 4x
Write an equation for the relationship shown below: y = kx
Write an equation for the relationship shown below: y = kx
y = 2x
Write the equation for this relationship in the form of y = kx
Write the equation for this relationship in the form of y = kx
y = 5x
Write the equation for the relationship in the form of y = kx
Write the equation for the relationship in the form of y = kx
y = 10x
Bailey ran 5 miles in 2 hours, 15 miles in 6 hours, and 25 miles in 10 hours. What is the equation for this relationship? y = kx
Bailey ran 5 miles in 2 hours, 15 miles in 6 hours, and 25 miles in 10 hours. What is the equation for this relationship? y = kx
| hours | miles |
| 2 | 5 |
| 6 | 15 |
| 10 | 25 |
y = kx
5 = k(2)
5/2 = k/2
k = 2.5
y = 2.5k
The THREE ways we have used to figure out if two ratios are proportional?
Hint: What have we done to find the constant of proportionality?
The THREE ways we have used to figure out if two ratios are proportional?
Hint: What have we done to find the constant of proportionality?
1. Ratio tables (with constant of proportionality)
2. Graphs (straight line through origin)
3. Formula (y = kx)
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