1. ## Gradient-intercept form of a plane?

Hi Does anyone know what is meant by "the gradient-intercept form of a plane"?

I have found the general form of the equation which is $\displaystyle 10x-3y-11z=-20$, but I've never heard of a gradient-intercept form before. I'm a math tutor trying to help someone with their homework and I stumbled upon this new term.

I make use of gradients for tangent planes, but ...

2. ## Re: Gradient-intercept form of a plane?

Originally Posted by VonNemo19;684849I have found the general form of the equation which is [TEX
10x-3y-11z=-20[/TEX], but I've never heard of a gradient-intercept form before.
I have never seen that term. But here is a guess.
$\displaystyle \frac{-10}{20}x+\frac{3}{20}y+\frac{11}{20}z=1$

3. ## Re: Gradient-intercept form of a plane?

Maybe something like (I'm guessing here, too)

$\displaystyle \hat{n}\cdot(\mathbf{r}-\mathbf{r}_{0})=0,$

where $\displaystyle \hat{n}$ is your gradient, and $\displaystyle \mathbf{r}_{0}$ is the intercept? The second is definitely a point in the plane.