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 Dependent Variable

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# Point-Slope Form for the Equation of a Line

Example

Find the equation of the line that passes through the points (-2, 7) and (6, 3). Write your answer in point-slope form.

Solution

To find the equation in point-slope form, we first find m, the slope of the line.

 Let (x1, y1) = (-2, 7) and (x2, y2) = (6, 3). m Substitute the values in the slope formula. Simplify. Reduce. The slope of the line is . Now that we have the slope and a point, we can use the point-slope form to find the equation of the line. y - y1 = m(x - x1) Substitute for m. We can substitute either given point for (x1, y1). Letâ€™s use (6, 3). y - y1 Therefore, substitute 6 for x1 and 3 for y1. y - 3 The point-slope form of the equation of the line that passes through (-2, 7) and (6, 3) is Note:

If we had used the other point, (-2, 7), we would have obtained: This equation is equivalent to 