The slope of a line and the angle it makes with the x-axis, the angle between two lines, parallel and perpendicular lines, and collinear points. Then the equation of a line in point-slope, two-point, slope-intercept and intercept forms.
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Created by StemPy LabThe slope of a line measures how steeply it climbs: the change in divided by the change in between any two of its points. It equals , where is the angle of inclination, measured from the positive -axis. A vertical line has no slope. The acute angle between lines of slopes and has .
Two lines are parallel when their slopes are equal, and perpendicular when the product of their slopes is . Horizontal and vertical lines need care, because a vertical line has no slope. Three points lie on one straight line, which we call collinear, when the slope of the first pair equals the slope of the second pair.
A point is on a line when its coordinates satisfy the line's equation. Four standard forms cover most lines: point-slope , two-point, slope-intercept , and intercept form . Horizontal lines are and vertical lines are . The section formula gives the point that divides a segment in a ratio.
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