Equations of lines

Interpret positions and distances using line equations and slopes.

Meaning

A line equation is a relationship satisfied by every point on it. In is slope. The general form with a and b not both zero, also represents vertical lines.

Example

The line through with slope 3 is also satisfies it and lies on the line.From the reference point (2,1), the horizontal change is x−2 and the vertical change y−1. The latter is three times the former, giving y−1=3(x−2); the reference point itself also satisfies it.A vertical line such as has undefined slope. Not every line has a real-valued slope.

Practice for this concept

Scope and references

Topics

Slopes and equations, parallelism, perpendicularity, point-to-line distance

Learning goal

Interpret positions and distances using line equations and slopes.

Helpful background

Explore slope, linear-function equations, and parallel/perpendicular conditions.