[SOUND] Let's look at Functions and the Vertical Line Test.

Let's determine whether the following equation defines y as a function of x.

Now, remember that in an equation of two variables, if each value of the

independent variable corresponds exactly one value of the dependent variable, then

the equation defines a function. In other words, if each allowed value of

x maps. To exactly one value of y, then the

equation defines y as a function of x. So solving our equations for y gives us

3y = 2x - 6. And then dividing both sides by 3, gives

us that y, is equal, to 2 minus 6 divided by 3, or 2.

Now, for each input Of the independent variable x, there will exactly one unique

output y. So, yes, this equation does define y as a

function of x. So yes, y is a function of x.

Now, another way to reach this conclusion is to think of the graph.

[SOUND] The graph of this equation, y = 2/3 x-2 is this line here.

Isn't it? It has y-intercept at -2. And a slope of two thirds which means we

go up 2 and over 3 neither something called that vertical line test, which

gives us a way to determine whether in a quotient defines y as function of x by

looking at it. It's graph.

And what it said is that an equation defines a function if each vertical line

in the rectangular coordinate system passes through, at most, one point on the

graph. And so looking at our graph here, any

vertical line that we pass through. This graph will intersect the graph at

only one point, so it represents a function, and the reason this is true,

why this works, is because what is the equation of a vertical line? It is x

equal to something. And so if it hits that graph at only one

point, that means for that x value there's only one output y.

Alright, let's look at another example. [SOUND] Let's determine whether this

equation defines y as a function of x. Again, let's solve for y.

So we have y^2 = 9 - x^2, or y = +-sqrt(9 - x^2).

So no, this equation, does not define y as a function of x.