Question

How does `y=mx+b` work?

Answer 1

See below

Explanation:

`y=mx+b` is the slope intercept form of an equation describing a line.

So how do we use it?

The first part of the equation I want to look at is the `x` and `y`:

• for any value of `x` I choose to put into the equation, I will get a resulting `y`. For instance, let's say `x=0` and it works out that `y=2` - I'd have a point I could plot on graph. If I do that one more time, say like `x=1, y=3`, and I can connect the two dots and extend that to form a line that heads off to infinity in both directions.

So now let's talk about the `m` and `b` values.

• `b` is the y-intercept. Let's say for instance that `b=2`. This means that the line intersects the y-axis at `y=2`, meaning we have a known point on the line of `(0,2)`.

• `m` is the slope. One way to think of it is the fraction `"rise"/"run"`. Let's say `m=1` - what that says is that for every step up (the rise) we move to the right 1 (the run).

Now let's put it all together. Let's take `y=x+2`. We have `m=1, b=2`. We can plot the y-intercept `(0,2)` and then move up 1 and to the right 1, which gives us `(1,3)`. Plot those and you can connect the dots.

We can also look at any value of `x`, say for instance `x=37`. We can see that `y=39`, and so we have a point `(37,39)`.