How do you know if an equation is linear or non-linear?

An equation is considered linear, if it is in the form of

`y=mx+b`

where `m` is the slope of the equation, and `b` is the y-intercept.

Notice how here, `x` can only be to the power of `1`.

In here, the conditions are just simply: `m,b\inRR`

Some examples include `y=5x+4`, `y=x-2`, `y=0`, and even some like `x=1`.

Let me graph them so that you can see:

`y=5x+4`
graph{5x+4 [-10, 10, -5, 5]}

`y=x-2`
graph{x-2 [-10, 10, -5, 5]}

`y=0`

![https://www.desmos.com/calculator]()

`x=1`

![https://www.desmos.com/calculator]()

As you can see here, all of the following equations are represented using a straight line. An equation is considered "non-linear" is when it is not graphed using straight lines. Some examples include `y=3x^2+1`, `y=2x^3-3`, `y=x^5+43`.

See what they have in common? They all have their first `x` with a power greater than `1`.

When we graph them, they are not going to be a straight line.

`y=3x^2+1`

graph{3x^2+1 [-10, 10, -5, 5]}

`y=2x^3-3`

graph{2x^3-3 [-10, 10, -5, 5]}

`y= x^5+43`

graph{x^5+43 [-22.79, 28.18, 29.24, 54.72]}

In conclusion, a linear equation will always be in the form of `y=mx+b`, where `m` is the slope of the equation, and `b` is the y-intercept of the equation.