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There are several ways, depending on the form of linear equation you want. I prefer the slope-intercept form, y = mx + b. Given two points, (x1, y1) and (x2, y2), we can calculate the values of m and b. The slope is m = (y2 - y1)/(x2 - x1). Plugging this and the coordinates of one of the points (say, (x1, y1)), we get
b = y1 - mx1.
But you are probably more interested in the two point form (for obvious reasons). This is basically an equation of the slope at a general point (x, y) with that at (x2, y2), namely (y - y1)/(x - x1) = (y2 - y1)/(x2 - x1).
To write a linear equation given two points, you can first calculate the slope using the formula: slope = (y2 - y1) / (x2 - x1). Once you have the slope, you can choose one of the points to substitute into the point-slope form of a linear equation: y - y1 = m(x - x1), where m is the slope and (x1, y1) is one of the points.
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the Equation of a Line Given That You Know Two Points it Passes Through.
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