Forms of linear equations, and parallel and perpendicular lines

A line can be written in several equivalent forms. Slope-intercept form, y = mx + b, shows the slope m and y-intercept b. Point-slope form, y - y1 = m(x - x1), is handy when you know a slope and one point (x1, y1). Standard form, Ax + By = C, makes intercepts easy to find. For example, the line through (2, 3) with slope 4 is y - 3 = 4(x - 2), which simplifies to y = 4x - 5, or 4x - y = 5 in standard form. Parallel lines have equal slopes, and perpendicular lines that are neither horizontal nor vertical have slopes that are negative reciprocals (their product is -1), while a horizontal line is perpendicular to a vertical one, so the line through (0, 1) perpendicular to y = 2x + 3 has slope -1/2 and equation y = -(1/2)x + 1. A horizontal line through (h, k) is y = k (slope 0), and a vertical line is x = h (undefined slope). Given two points instead, first find the slope, m = (y2 - y1)/(x2 - x1), then use either point: through (1, 2) and (3, 8), m = 6/2 = 3, so y - 2 = 3(x - 1).

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