Lines
The slope of a line passing through points [[$x_1, y_1 $]] and [[$x_2, y_2 $]]:
[[$ k = \text{tan} \space \alpha = \dfrac{y_2-y_1}{x_2-x_1} $]]
A line is
[[$ax + by + c = 0$]]
Solved form of the equation of a line:
[[$y = kx + b$]], where [[$k$]] is the slope an [[$b$]] is the constant term (the [[$y$]] coordinate of the interesection point of the line and the [[$y$]]- axis).
The equation of a line parallel to the [[$x$]]-axis:
[[$y = t$]], where [[$t$]] is the [[$y$]] coordinate of the intersection point of the line and the [[$y$]] axis
The equation of a line parallel to the [[$y$]]-axis:
[[$x = u$]], where [[$u$]] is the [[$x$]] coordinate of the intersection point of the line and the [[$x$]] axis
[[$ k = \text{tan} \space \alpha = \dfrac{y_2-y_1}{x_2-x_1} $]]
A line is
- ascending if [[$ k > 0 $]]
- descending if [[$ k < 0 $]]
- parallel to the [[$x$]]- axis if [[$k = 0 $]]
- parallel to the [[$y$]]- axis if [[$k$]] cannot be determined.
- The lines are parallel, i.e. [[$s_1||s_2$]], if [[$k_1=k_2$]] or lines are parallel to the [[$y$]]- axis.
- The lines are perpendicular to each other, i.e. [[$s_1 \perp s_2$]], if [[$k_1 \cdot k_2 = -1$]] or one line is parallel to the [[$x$]]- axis and the other to the [[$y$]]- axi.
[[$ax + by + c = 0$]]
Solved form of the equation of a line:
[[$y = kx + b$]], where [[$k$]] is the slope an [[$b$]] is the constant term (the [[$y$]] coordinate of the interesection point of the line and the [[$y$]]- axis).
The equation of a line parallel to the [[$x$]]-axis:
[[$y = t$]], where [[$t$]] is the [[$y$]] coordinate of the intersection point of the line and the [[$y$]] axis
The equation of a line parallel to the [[$y$]]-axis:
[[$x = u$]], where [[$u$]] is the [[$x$]] coordinate of the intersection point of the line and the [[$x$]] axis