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### Course: 8th grade (Illustrative Mathematics) > Unit 3

Lesson 2: Lesson 4: Comparing proportional relationships# Rates & proportional relationships example

Let's compare unit rates in equations and graphs. Learn how a change in 'x' affects 'y' in an equation like y = 6.5x, and see how this compares to the rate of change in a graph. Uncover why one might increase at a slower pace than the other. Created by Sal Khan.

## Want to join the conversation?

- This is very confusing. can someone explain it?(38 votes)
- You will have to be more specific find the spot in the video and ask about that part.(3 votes)

- what does ambiguous mean(11 votes)
- Ambiguous means unclear or having multiple meanings. You 𝘤𝘢𝘯 look it up.(17 votes)

- anyone else not get this?(17 votes)
- Yes! I don't understand well, too.(2 votes)

- im just so confused i don't understand very well(10 votes)
- How would you do it if it was,

A giraffe grows 3-10 inches per day,

Which of the following equations, where t represents time in days, and H represents height in centimeters, could be descriptions of the growth of the giraffes height?

H=1.1t

H=2.5t

H=7.1t

H=9.3t

Thanks for helping me!(5 votes)- So you said that the giraffe grows between 3-10 cm a day..

Where t = days an h = height.

So there can be more than one answer because we don’t how how much exactly it grows..

So the answers would be between 3 and 10.

3) H = 7.1t

4) H = 9.3t

Those were the only 2 possible answers in the given options..

Hope this helped(8 votes)

- This makes no sense please help(4 votes)
- So in the video the question is, "is y=6.5x a slower unit rate (the unit rate is 6.5)then the unit rate shown in the graph. The graphs unit rate is y=3.5x (where 3.5 is the unit rate). So if you compare the two unit rates, 6.5(sentence unit rate) and 3.5(graph unit rate), 3.5 is the slower unit rate. Hope this helps :}(10 votes)

- What if all of the rates are not equal would the answer still be the smae?(6 votes)
- It depends on the rates(4 votes)

- I don't get this. Can someone please help me?(4 votes)
- I can only help you if you tell me what you don't understand.(6 votes)

- You use the Show solution?(6 votes)
- But what if In the problem it is like this 17,000 compared to the for example(3,6) What do we do?(3 votes)
- Please elaborate(6 votes)

## Video transcript

Which is less-- the unit rate
of the equation y equals 6.5x or the unit rate of
the graph shown below? So when they're talking
about unit rate-- and they're actually a
little bit ambiguous here. They should have been
clearer in this question. I'm assuming they're
asking us about the unit rate at which y changes
with respect to x. Or how much does y
change for a change of 1 in x, the unit rate. And over here, you
see when x changes 1, y is going to change by 6.5. Every time x increases by 1,
y is going to increase by 6.5. Or you could say the unit rate
of change of y with respect to x is 6.5 for
every 1 change in x. In this graph right over
here, as x changes 1, as x increases 1, y increases it
looks like by about 3 and 1/2. x increases by 1, y
increases by 3 and 1/2. So the unit rate
of change here of y with respect to x is 3 and 1/2
for every unit increase in x. So this line is increasing at a
slower rate than this equation. Or y in this line is increasing
at a slower rate with respect to x than y is increasing with
respect to x in this equation right over here. So the unit rate of
the graph is less than the unit rate
of the equation.