Graphing proportional relationships example 2

We're asked to graph the proportional relationship shown in the table below.

And they give us a table of x values and the corresponding y values.

So we see when x is equal to 0, y is equal to 0.

Then they give us a bunch of other points.

When x is 3, y is 0.5.

When x is 6, y is 1.

So on and so forth.

So let's graph one of these that actually have integer values for both coordinates.

So when x is 6, y is 1.

So we only need 2 points to specify the line.

So we've actually graphed it.

But then they also ask us, "What is the slope of this line?"

And we just have to remind ourselves:

Our slope is our change in y for a given change in x.

So, for example – Or another way to think about it:

What is your change in y over your change in x?

So here, our x changed by 6.

It went from 0 to 6.

And our y changed by 1.

So our change in y over our change in x,

(which is the definition of slope),

our change in y is 1 when our change in x is 6.

We see that right over here.

Our change in y is 1 when our change in x is 6.

Let's check our answer.

We got it right.