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### Course: 7th grade (Eureka Math/EngageNY) > Unit 1

Lesson 2: Topic B: Unit rate and constant of proportionality- Intro to rates
- Unit rates
- Solving unit rate problem
- Solving unit price problem
- Constant of proportionality from equation
- Constant of proportionality from equations
- Identifying constant of proportionality graphically
- Constant of proportionality from graphs
- Constant of proportionality from table (with equations)
- Constant of proportionality from tables (with equations)
- Comparing proportionality constants
- Compare constants of proportionality
- Interpret proportionality constants
- Interpret constants of proportionality
- Worked example: Solving proportions
- Solving proportions
- Writing proportions example
- Writing proportions
- Proportion word problem: cookies
- Proportion word problem: hot dogs
- Proportion word problems
- Equations for proportional relationships
- Writing proportional equations from tables
- Writing proportional equations
- Interpreting graphs of proportional relationships
- Identify proportional relationships from graphs
- Interpreting graphs of proportional relationships
- Interpret constant of proportionality in graphs

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# Constant of proportionality from equation

Sal identifies the constant of proportionality from equations.

## Want to join the conversation?

- does anyone else not get this 😌🙃(92 votes)
- Is there a specific reason that you always solve for y, and not x?(32 votes)
- You normally solve the constant of proportionality for first number to second number.(9 votes)

- how are you able to tell 4 is not 1/2 if it only says 4/x , the x could =8?(17 votes)
- y = 4/x

What this equation tells you is that for whatever value of x, y will equal 4 divided by that value.

Here, x and y are variables, their value changes.

This means that the y-value depends on the x-value. They need not be fixed : x and y can equal anything, but their product will always be four.

The constant of proportionality here is the 4, because it is the only thing which has a fixed value.

P.S. : This is a different type of proportion, called**inverse**proportion. Here, as one variable increases, the other decreases and vice-versa. The equation is in the form of y = k*1/x.

Hope this helps :)(3 votes)

- Honestly this is kinda lame like were never gonna do this in the real world Right?(13 votes)
- My mom randomly makes me Do it(11 votes)

- why do we do these(12 votes)
- FOR REAL why do we do these are we gonna do this in real life like(13 votes)

- please help me i know nothing(11 votes)
- at1:58how did you get 1/2 dont u do 6 divided by 3 is 2? im a little confused?(2 votes)
- 3/6 is the same as 1/2 because 3 times 2 is 6(13 votes)

- What happens if the problem your trying to solve has a decimal? For Example: y = 2.5x ?(4 votes)
- That's ok. The constant of proportionality can be a decimal, fraction, integer, or any real number.(8 votes)

- Question one doesn't make sense to me,

So we have

4y = 8x

so for Y=KX We find what times X = Y or Y/X. 4/8 (Y/X) not 8/4 (X/Y)

So Y=1/2 . 8X = 4,

but Sal wrote Y=2X 2 . 8X = 16 not our Y = 4(4 votes)- If you are starting with: 4y=8x, you need to divide both sides by 4 to find the constant of proportionality. You get:

y = 2x

The constant of proportionality = 2

The value of Y will always be 2 times the value of X.

Hope this helps.(6 votes)

- Sometimes I get my variables mixed up and end up thinking the constant of proportionality/unit rate of change/slope is, for example, 3 when it is supposed to be 1/3. when there is an x and a y I know what to do because I remember xk=y, but when I've got a word problem where the variables are z and h or n and j, I get all mixed up again and before I know it I've got hours per mile instead of miles per hour! Any tips on how to remember which one is which?(2 votes)
- You may find it helpful to keep track of the units of measurement your are working with. Label the numbers with miles and hours so you can see your result in units. If the problem asks your for miles/hour, then you know you need to divide the miles by the number of hours.

Hope this helps.(10 votes)

## Video transcript

- [Instructor] We are
asked, "What is the constant "of proportionality in the
equation 4y is equal to 8x?" Pause this video and have
a go at this question. All right, so we might be used to seeing constants of proportionality when we have equations in
a slightly different form. A constant of proportionality is what do you multiply x by to get to y? So y would be equal to our constant of
proportionality times x. But this isn't written in that form, so what we do is
manipulate it a little bit so that we can see it in that form. And the obvious thing is we
just need to solve for y. So right now it says 4y is equal to 8x. Well, if we wanna solve for y, we can just divide both sides by four, and we are left with y is
equal to eight divided by four, which is two times x. Well, now the constant of
proportionality jumps out at us. To get y, we have multiply x by two. That is our constant of proportionality. Let's do another example. Here we're asked, "Which
equation has a constant "of proportionality equal to 1/2?" Again, pause the video. Try to answer it yourself. Okay, so I'm just gonna
go equation by equation and calculate their
constants of proportionality and see which one has a constant of proportionality equal to 1/2. So this one right over here,
choice A clearly has a constant of proportionality of 1/8,
so we can just rule that out. Equation B right over here
clearly has a constant of proportionality of four, not 1/2, so we can rule that one out. Let's see, the constant of
proportionality for equation C, if we wanna solve for y, we
could divide both sides by six. And so we're gonna get y
is equal to 3/6 times x. Well, 3/6 is the same
thing as 1/2 times x, and so there you have it. We have a constant of
proportionality of 1/2. That's the choice I like. And we can verify that
this one doesn't work. If you wanna solve for y, you
divide both sides by three, and you get y is equal to
nine divided by three is 3x, so here our constant of
proportionality is three, so we can feel good about choice C.