How does #y=mx+b# work?

1 Answer

Answer:

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)#.