Writing Equations of Lines – The Point-Slope Formula

Point Slope Form

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Students learn to write the equation of a line given a point on the line and the slope of the line, by using the point-slope formula, which states that given a point (x1, y1) and a slope m, the equation of the line can be written as y – y1 = m(x – x1). For example, if a line passes through the point (3, -2), and has a slope of 4, its equation can be written: y + 2 = 4(x – 3). From here, the equation can be converted to either slope-intercept or standard form. Note that a horizontal line passing through a given point has the equation y = the y-coordinate of the given point, and a vertical line passing through a given point has the equation x = the x-coordinate of the given point.
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