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## 8th grade (Eureka Math/EngageNY)

### Course: 8th grade (Eureka Math/EngageNY) > Unit 4

Lesson 2: Topic B: Linear equations in two variables and their graphs- Rates & proportional relationships example
- Rates & proportional relationships: gas mileage
- Rates & proportional relationships
- Graphing proportional relationships: unit rate
- Graphing proportional relationships from a table
- Graphing proportional relationships from an equation
- Graphing proportional relationships
- Points on the coordinate plane examples
- Testing solutions to linear equations
- Solutions to 2-variable equations
- Graphing a linear equation: 5x+2y=20
- Complete solutions to 2-variable equations

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# Graphing proportional relationships from an equation

Sal graphs the equation of a line that represents a proportional relationship given an equation. Created by Sal Khan.

## Want to join the conversation?

- i still don't understand how to do these :((28 votes)
- First start with an equation, like y = 4x. Next, plug in a number as x, like 5. Since you would need to multiply it by 4 to find y,(hence the 4x), That means that the y would be equal to 20.

So, in the end, a point on your graph would be (5,20). To find other points, you would plug in any other number as x, and that would get you your line.

Does that help?(4 votes)

- dude i dont u n d e r s t a n d, please help(16 votes)
- I don't get any of this. PLZ help!(12 votes)
- i dont understand(6 votes)
- How can I help you? Reply back please.(6 votes)

- I look in the question bar for help and everyone's as lost as I am.(4 votes)
- Plus all these comments are ancient, no one from my class is active on here apparently. They probably need to get upvoted to be seen so I don't think anyone's reading my comments either.(10 votes)

- At2:50, how can Y change 12.5?(6 votes)
- At2:50Y doesn't change 12.5 it changes by 5 for every time the x changes by 1(3 votes)

- is math related to science(1 vote)
- Yes, you will encounter a lot of mathematical equations and calculations in chemistry and physics.

Have a blessed, wonderful day!(12 votes)

- If you read this your a dad(6 votes)
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──────████──██████████(5 votes)

## Video transcript

We're asked to graph y
is equal to 2.5 times x. So we really just have to
think about two points that satisfy this equation here,
and the most obvious one is what happens when x equals 0. When x equals 0, 2.5
times 0 is going to be 0. So when x is 0, y is
going to be equal to 0. And then let's just
pick another x that will give us a y that
is a whole number. So if x increases by 1, y
is going to increase by 2.5. It's going to go
right over there, and I could graph
it just like that. And we see just by
what I just said that the unit rate of change
of y with respect to x is 2.5. A unit increase in x, an
increase of 1 and x, results in a 2.5 increase in y. You see that right over
here. x goes from 0 to 1, and y goes from 0 to 2.5. But let's increase
x by another 1, and then y is going to increase
by 2.5 again to get to 5. Or you could say, hey, look,
if x is equal to 2, 2.5 times 2 is equal to 5. So this is a legitimate
graph for this equation, but then they also
tell us to select the statements that are true. So the first one is
the equation does not represent a proportional
relationship. Well, this is a
proportional relationship. A proportional
relationship is one where, first of all, if
you have zero x's, you're going to have zero y's, where y
is equal to some constant times x. And here, y is equal
to 2.5 times x. So this is definitely a
proportional relationship, so I'm not going to check that. The unit rate of the
relationship is 2/5. So I'm assuming--
this is a little ambiguous the way
they stated it. I'm assuming they're saying
the unit rate of change of y with respect to x. And the unit rate of change
of y with respect to x is, when x increases
1, y changed 2.5. So here they're saying when x
changes by 1, y changes by 0.4, 2/5 is the same thing as 0.4. This should be 5/2. 5/2 would be 2.4. So this isn't right as well. The slope of the line is 2.5. Well, this looks right. Slope is change in
y over change in x. When x changes 1, y changes 2.5. So change in y, 2.5,
over change in x, 1. 2.5 over 1 is 2.5. And you could also
see it looking at the form of
this equation. y is equal to-- this is
the slope times x. So that's right. A change of 5 units in x results
in a change of 2 units in y. Well, let's test that idea. We know when x is 0, y is 0. So if x goes from 0 to 5,
what's going to happen to y? Well, y is going
to be 2.5 times 5. 2.5 times 5 is 12.5. So y would not just change 2. It actually would change 12.5. So this isn't right. A change of 2 units in x results
in a change of 5 units in y. Well, we see that. A change in 2 units of x results
in a change of 5 units in y. That's exactly what we
graphed right over here. These two points show that. So this is definitely true.