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### Course: 8th grade > Unit 3

Lesson 13: Linear and nonlinear functions- Recognizing linear functions
- Linear & nonlinear functions: table
- Linear & nonlinear functions: word problem
- Linear & nonlinear functions: missing value
- Linear & nonlinear functions
- Interpreting a graph example
- Interpreting graphs of functions
- Linear equations and functions: FAQ

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# Interpreting a graph example

Learn to interpret the graphs of a linear functions. Created by Sal Khan.

## Want to join the conversation?

- can u plz give more examples because every problem isn't always worked out the same as this one(67 votes)
- I know right with my problem it is exactly what you mean.(11 votes)

- they need more examples I still don't understand what to do cause all I get for an example is this none of the questions are like this.(39 votes)
- Math reminds me of doing homework..... Non-existent...(22 votes)
- please more examples this program makes no sense(16 votes)
- Man, I still don't get this I need someone to explain it more clearly - not saying that sal doesn't do a good job. Like I don't get how at0:41he said we move 1 in the x-direction we move -1 in the y direction(6 votes)
- To find the slope of a line you need to look at the rise over run.If a line is tilted to the right the slope will be positive and if its going to the left it will be negative. to find the slope he is looking for points that the line goes through, you don't always only move 1 unit it depends on how far apart the points are. for easier viewing some people draw whats called a triangle. This shows two points that the line goes through. The triangle will also make it easier to look at the rise (y) over run (x).(10 votes)

- how do you interpret a graph(9 votes)
- Yes, this video is given as the "help" on a question with a loopy radio frequency type line that asks for "y-intercept", "smallest possible x-intercept", and listing the items in negative x territory as fractions of pie. Not so helpful...(8 votes)
- This so confusing I don’t understand any of it can someone help me? Please.(6 votes)
- i really want to, but i cant help you without showing you :( all i can say is just follow the number line and go up down left right until you stumble upon a part of the graph line.(2 votes)

- IDK why math makes me feel like i have one brain cell(6 votes)
- Why didn't Sal make a video on how to interpret distance-time graphs as well? These graphs aren't the only ones you get.(5 votes)

## Video transcript

The illustration below shows the
graph of y as a function of x. So that's this graph
right over here. And then they start to
ask us some questions. Complete the sentences based
on the graph of the function. So this axis is our
y-axis, the vertical axis. Horizontal axis is x-axis. Initially, as x increases--
so let's think about it. Initially, so when we start from
x equals 0 and x is increasing, what's happening to y? Well, y is decreasing. So y decreases. So as x increases
initially, y decreases. The slope of the graph is equal
to blank for all x between x equals 0 and x equals 3. So x equals 0 and x equals
3, what's the slope? Well, every time we move
1 in the x direction, we move down in the y direction. We go negative 1
in the y direction. Move up 1 in the x
direction, we go negative 1 in the y direction. So our change in y over our
change in x-- our change in y is negative 1 whenever
our change in x is 1. So our change in
y over our change in x, which is the definition
of slope, is negative 1/1. So it's negative 1. And we see that. Every time x increases
by 1, y decreases by 1. Starting at x equals 3,
y blank as x increases. So starting at x equals 3,
y increases as x increases. As x increases, y is increasing. So y increases as x increases. The slope of the graph is equal
to blank for x between 3 and 5. So when x increases by
1, y is increasing by 3. So change in y is
3, change in x is 1. Slope is change in y over
change in x, which is 3/1. So the slope here is 3. Every time x increases
by 1, y increases by 3. For x between x equals 0 and
x equals 4, y-- let's see, we can pick less than or equal
to, greater than or equal to, or equal. So for x equals
0 and x equals 4, y is less than or equal to 0. So let's do less
than or equal to 0. And then they say,
for x between x equals 4 and x
equals 8-- well, then y is greater than or equal to 0. So let's make sure
that we didn't make any careless mistakes here. Let's check our answer. We got it right.