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### Course: Operations and Algebraic Thinking 222-226 > Unit 1

Lesson 2: Constant of proportionality- Introduction to proportional relationships
- Identifying constant of proportionality graphically
- Constant of proportionality from graph
- Constant of proportionality from graphs
- Identifying the constant of proportionality from equation
- Constant of proportionality from equation
- Constant of proportionality from equations
- Constant of proportionality from tables
- Constant of proportionality from tables
- Constant of proportionality from table (with equations)
- Constant of proportionality from tables (with equations)

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# Constant of proportionality from table (with equations)

Sal identifies the constant of proportionality from table.

## Want to join the conversation?

- so when your doing the table do you always times by 2.5(31 votes)
- You only use the constant of proportionality that is given in the table.It varies in each problem.(52 votes)

- For a proportionality, do you always find the ratio from the left to the right, or in some cases do you find the ratio from right to left, and if you do, how do you know which direction you take the ratio from in a problem(left to right or right to left)(33 votes)
- so from left to right in most cases is is multiplication but right to left in most cases in division.(9 votes)

- he just took 2.5 out of nowhere like what(13 votes)
- It doesn't come out of nowhere. As Sal tells you in the video, you start with the value of "x" and you find the value that you can multiply with "x" to create the y-value.

Or, use the forumula: y=rx

If x=4 and y=10, plug in those values: 10=4r

Solve for "r" by dividing by 4: r = 10/4 = 2.5

Hope this helps.(33 votes)

- what if the numbers on the right are fractions(15 votes)
- By the right you mean Y, right?

Example:

If we have 1/3 as Y, and we have 2 as x, it might just be easier for you to divide the fractions/turn the fraction into a decimal, and then divide the Y by the X.

So with my example, 1/3

1/3 = 0.3 repeating

Then you would divide that by whatever X is.

So, in simple words, turn Y into a decimal first, and then divide Y by X.

Hope this helped!

If it did, can you pls give me a vote? :)(18 votes)

- What do I do if the video doesn't work?(11 votes)
- so basically, you have to find a specific number to solve for each problem with the same number?(13 votes)
- yes but that specific number is called the constant of proportionality and its what fits the entire question together(2 votes)

- thi is to hard for my tiny brain lol(14 votes)
- But what if "y" is a mixed number? Would you convert it to a fraction and then try to make it into a decimal? I'm confused :/(6 votes)
- To turn a mixed number into a decimal without turning it into an improper fraction, all you have to do is:

For example we have a mixed number:

3 4/5

Take the whole number from the fraction which is 3, and then solve the fraction:

4/5 = 0.8

Add the result to the whole number and there you have it:

3 + 0.8 = 3.8(9 votes)

- how did yall get 2.5 im not supposed to just know that(7 votes)
- In the start, we had 10/4, that got simplified to 5/2, that got simplified to 2.5/1, and that equals 2.5.

Hope that helped!(4 votes)

- I still have a bit of trouble with this, but I'm pretty sure that's just because of my very miniscule brain.(7 votes)
- you do not have a miniscule brain everyone has a perfect sized brain you just have to apply yourself and put what you learned in your (what I like to call) memory banks(3 votes)

## Video transcript

- [Instructor] We're told the quantities x and y are proportional, and then they give us a
table where they give us a bunch of x's and they give
us the corresponding y's. When x is four, y is 10. When x is five, y is 12.5,
and so on and so forth. Find the constant of proportionality, r, in the equation y is equal to r times x. So pause this video and see
if you can figure that out. All right so we wanna find the constant, the constant of proportionality, I sometimes have trouble saying that, r, where if I for any x, if I multiply it by r I get y. Well we just have to
look at each of these x's and figure out well what
are we multiplying by to get to y. So what do I have to multiply
four by to get to 10? Well if you multiply it by 10/4, if you multiply it by 10/4,
then you're gonna get to 10. And 10/4 is the same thing
as multiplying it by, let's see that is 2 1/2. So this is times 2 1/2. So let's see does that hold? In every case if I multiply by 2 1/2, if I multiply x by 2 1/2, do I get y? So five times 2 1/2, five times two is 10, and
then another 1/2 is 2.5. It indeed does equals 12.5. Five times 2.5. And then here 10 times 2.5 is clearly 25. And you can work it out by hand. I did the little bit of the
multiplication in my head, but you can see in every case, I take my x, I multiply
it by 2.5, I get my y. So in every case I take
my x and multiply it by the constant of
proportionality 2.5, I get my y. So what's the constant of proportionality? It is 2.5.