# Work in progress... Not yet ready for public consumption; please check back in a couple of months. Ideally this will be usable for school this coming fall. ## Example The end result of the following example will be similar to what you see [over here](https://colbyn.github.io/school-notes-spring-2020). ``` ... \note[boxed] { \h3{Symmetric Equation of a Line} Given \equation { t &= \frac{x - x_1}{x_2-x_1} = \frac{x - x_1}{\Delta_x}\\ t &= \frac{y - y_1}{y_2-y_1} = \frac{y - y_1}{\Delta_y}\\ t &= \frac{z - z_1}{z_2-z_1} = \frac{z - z_1}{\Delta_z} } Therefore \equation { \frac{x - x_1}{Delta_x} &= \frac{y - y_1}{\Delta_y} = \frac{z - z_1}{\Delta_z}\\ \frac{x - x_1}{x_2-x_1} &= \frac{y - y_1}{y_2-y_1} = \frac{z - z_1}{z_2-z_1} } \hr \h4{Rationale} We rewrite \{r = r_0 + a = r_0 + t v} in terms of \{t}. That is \equation{ x &= x_1 + t(x_2-x_1) = x_1 + t\;Delta_x\\ t\;Delta_x &= x - x_1 = t(x_2-x_1)\\ t &= \frac{x - x_1}{x_2-x_1} = \frac{x - x_1}{Delta_x} \\\\ y &= y_1 + t(y_2-y_1) = y_1 + t\;\Delta_y\\ t\;\Delta_y &= y - y_1 = t(y_2-y_1)\\ t &= \frac{y - y_1}{y_2-y_1} = \frac{y - y_1}{\Delta_y} \\\\ z &= z_1 + t(z_2-z_1) = z_1 + t\;\Delta_z\\ t\;\Delta_z &= z - z_1 = t(z_2-z_1) \\ t &= \frac{z - z_1}{z_2-z_1} = \frac{z - z_1}{\Delta_z} } } \!where { {\Delta_x} => {\colorA{\Delta_x}} {\Delta_y} => {\colorA{\Delta_y}} {\Delta_z} => {\colorA{\Delta_z}} {x_1} => {\colorB{x_1}} {y_1} => {\colorB{y_1}} {z_1} => {\colorB{z_1}} } ```