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### Course: 7th grade > Unit 1

Lesson 4: Graphs of proportional relationships# Interpreting graphs of proportional relationships

Worked example interpreting graphs of proportional relationships.

## Want to join the conversation?

- It looks impossible for mankind to be able to invent such a complex world of math while everything fits together and makes sense. While not having any mistakes.(12 votes)
- I agree, I can only study what's already invented I feel like my mind can't go beyond that to discover or make more math. it makes u wonder how their brains worked, what they were thinking, considering when making these concepts.(14 votes)

- whats the diffrence between linear and porportional(12 votes)
- linear means it is a line proportional means it is a line that goes to (0,0)(9 votes)

- k for constant 👍(12 votes)
- whats the difference between linear and porportional(7 votes)
- Linear lines are straight lines on a graph

proportional lines are straight lines on a graph that start at the origin

also linear lines are defined by the equation y = mx + b

proportional lines are defined by the equation y = kx

hope this helped(11 votes)

- Hello? Anybody here? All these comments are really old.(7 votes)
- If you hit the sort by button above the comments you will see comments from a little more recently.(7 votes)

- and when do we use this in life?(5 votes)
- Honestly? Almost never. But if you want a well-paying job later in life, that'll most likely require college experience. And to get into college you'll need to take tests. And these tests will be about subjects like this. So really what you are learning now in school and on Khan will be impacting you on unimaginable scales later in life.(10 votes)

- how would i do this on a bigger graph in the thousands(4 votes)
- There are two ways to scale a graph, instead of going by 0, 1, 2, 3 (and negatives to the left or down), the scale can be changed to 0, 1000, 2000, 3000, etc, including negatives without even having to change the size of the graph. The other option is to define each of the x and y axis in terms of larger numbers such as x represents dollars (in thousands).(5 votes)

- who decided to put letters in math?(3 votes)
- The people who needed to express that they didn't know one of the numbers in the equation, but still needed to write an equation. It's actually quite useful and fun in my opinion, figuring out the variable is kind of like a puzzle, so I'm quite glad they put letters in math!(2 votes)

- The second one is tricky(4 votes)
- What does the K mean in this Question?(3 votes)
- This is algebra. K is an algebraic term.(2 votes)

## Video transcript

- [Instructor] We are told
the proportional relationship between the number of
hours a business operates and its total cost of electricity is shown in the following graph, all right. Which statements about the graph are true? Choose all answers that apply. So pause this video and see
if you can figure this out. All right, now let's do this together. And before I even look at the choices, let me analyze this a little bit. It is a proportional relationship. So we know that our total
cost, let me write it here. Our total cost is going to be equal to some
constant of proportionality times our number of hours. And we can even figure out what that constant of
proportionality is going to be, because they give us this point A. We know that when our hours are four, so when this is four right over here, our total cost is $120. $120. So what times four is equal to 120? Well, we know that this k must be 30, 'cause 30 times four is 120. So we can write that
proportional relationship where our total cost is going to be equal to our constant of proportionality, 30, times our number of hours. Number of hours. So let's see which of these choices, and it might be more than one, say this or describe what's going on here. So choice A, the y-coordinate of point A, so point A is at the point four comma 120, so the y-coordinate is the 120. That's the total cost when you run your business for four hours. The y-coordinate of point
A represents the total cost of electricity when the business
operates for four hours. Yes, that is exactly
or very close (laughs) to what I just said, so I like this one. The total cost of electricity is $35 when operating the business for one hour. So let's go to one hour here. This is going to be the total cost. Now, you might say, hey, this
looks kinda close to $35, but that's why it was useful for us to write this relationship
right over here, because what we see is that
our total cost is going to be 30 times our number of hours. Our total cost here is actually
going to be 30, not 35. And it actually does look smack dab in between 20 and 40 versus
a little bit closer to 40. So this one is not going to be true. And we're not gonna
select none of the above, 'cause we actually did
select one of the above. And we're done.