Question

What are the various forms of the equation for a line? How do two slopes relate parallel and intersecting/perpendicular lines?

Accepted Answer

**standard form:** $$Ax + By + C = 0$$, where *A*, *B*, and *C* are constants.\
**slope-intercept form:** $$y = mx + b$$, where *m* is the slope, defined as $$m = \frac{y_2 - y_1}{x_2 - x_1}$$, where $$(x_1, y_1)$$ and $$(x_2, y_2)$$ are two points on the line, and *b* is the *y*-intercept.   
**point-slope form:** $$(y - y_1) = m(x - x_1)$$, where *m* is the slope, and $$(x_1, y_1)$$ is a point on the line.\
Parallel lines share the same slope. Intersecting lines have different slopes, and in the special case where the slopes are negative reciprocals of each other, the lines are perpendicular (they intersect at a $$90^\circ$$ angle).

Flashcard 2 - Next Generation Advanced Algebra and Functions Flashcard Set for the ACCUPLACER Test

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