Formulas
What is the formula to find k (the constant of proportionality)?
k = Right/Left
or
k = y/x
If there is a ratio of 2:3 cups of blue paint to yellow paint...How many cups of yellow paint do they need to make the same color with 6 cups of blue?
9!
Is y = 3x proportional?
For a graph to be proportional, it must...
-be a straight line
-cross through the origin (0,0)
What is the x-coordinate of the following point
(3,9)
3
What is the formula for a proportional relationship?
y = kx
x y What is k for this table?
2 3
4 6
8 12
k = 3/2 or 1.5
Is y = 3x -10 proportional?
no! (it has an added or subtracted term)
The point (6,16.5) is on a proportional graph, what is the constant of proportionality?
k = 16.5/6 -->
2.75
What is the y-coordinate of the following point
(4,16)
16
fill out the right side of the table
3 ?
7 ?
12 5
k = 5 /12
multiply all the numbers on the left side by 5/12
3 15/12 (or 1.25)
7 35/12 (or 2.91)
12 5
What is the equation of the proportional relationship where k = 52?
y = 52x
how do you determine which line represents a FASTER relationship?
Which one is steeper!!
if x = days of rest
and y = hours of sleep,
interpret what the point (7, 56) means in the context of the problem.
For every 7 days of rest, you get 56 hours of sleep.
x y
? 7.5
5 12.5
? 22.5
k = 12.5/5 ----> k = 2.5
divide all the values on the right by 2.5
3 7.5
5 12.5
9 22.5
x = cups of lemon juice
and y = cups of water. Their relationship can be modeled by y = 1.5x
If you have 12 cups of lemon juice, how many cups of water do you need?
18 cups of water!
The point (1 , 2.5) is on a graph. What would be the equation of the proportional relationship?
y = 2.5x
free response
When would it be better to use a table than an equation or a graph?
When you are interested in only a few points/ratios.
x = cups of lemon juice
and y = cups of water. Their relationship can be modeled by y = 1.5x
If you have 9 cups of water, how many cups of lemon juice do you need?
6!
The point (1, 2.5) is a on the graph of a proportional relationship.
Is the point (4, 9) on the graph?
NO!
We can use k to see that when x =4, in order for the point to be on the graph, y must = 10.
:)
(: