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# Interpreting a graph example

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.