# How does y=mx+b work?

See below

#### Explanation:

$y = m x + b$ 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 $\left(0 , 2\right)$.

• $m$ is the slope. One way to think of it is the fraction $\text{rise"/"run}$. 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 $\left(0 , 2\right)$ and then move up 1 and to the right 1, which gives us $\left(1 , 3\right)$. 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 $\left(37 , 39\right)$.