Procedure ‐ Two Points on Equation Line

Goal

The goal of the two points on equation line procedure is to find two points on a line given by an equation.

Inputs

The inputs for this procedure are:

• aCoefficient: The $a$ coefficient of the line equation.
• bCoefficient: The $b$ coefficient of the line equation.
• cCoefficient: The $c$ coefficient of the line equation.

Outputs

The outputs of this procedure are:

• point1: The first point on the line.
• point2: The second point on the line.

Procedure

The procedure for this is as follows:

If $a = 0$ and $b = 0$ then the the equation is not a line and we throw an error.

If $a = 0$ then the equation is in the form of $by + c = 0$ and we can find a point on the line by setting $x = 0$ and solving for $y$. The point is then $[0, \frac{-c}{b}]$.

If $b = 0$ then the equation is in the form of $ax + c = 0$ and we can find a point on the line by setting $y = 0$ and solving for $x$. The point is then $[\frac{-c}{a}, 0]$.

If $a \neq 0$ and $b \neq 0$ then the equation is in the form of $ax + by + c = 0$ and we can find two points on the line by setting $x = 0$ and solving for $y$. The first point is then $[0, \frac{-c}{b}]$.

Now that we have one point on the line we can find the second point by moving by the directional vector of the line $\vec{v}$. The vector $\vec{v}$ the vector perpendicular to the normal vector of the line.

The second point is then $[0, \frac{-c}{b}] + \vec{v}$.