To write the equation of a line parallel to a given line through a given point:
- Find the slope of the given line.
- Use that slope and the point on the new line to write the equation of the new line.
y − y1= m(x − x1)
To write the equation of a line perpendicular to a given line through a given point:
- Find the slope of the given line.
- Use the opposite reciprocal of that slope and the point on the new line to write the equation of the new line.
y − y1= m(x − x1)
To write the equation of a horizontal or vertical line through a given point:
| Line Type | Slope of the LIne | Equation Form |
|---|---|---|
| Horizontal | Zero m = 0 |
y = number |
| Vertical | Undefined | x = number |
Relationships of horizontal and vertical lines to other horizontal and vertical lines:
| Line Type | Relationship to Horizontal Lines | Relationship to Vertical Lines |
|---|---|---|
| Horizontal | Parallel | Perpendicular |
| Vertical | Perpendicular | Parallel |
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