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How to Determine the Slope of a Line Passing Through Given Pair of Points

To graph a linear equation, which always produce straight lines, the equation needs to be converted to slope intercept form: y = mx + b, where "m" is the slope and "b" is the y-intercept. Both the "m" and "b" need to be known to put the equation in this form. If the "b" is unknown, but one point, point (x1, y1), is known, the point slope form can be used to get to slope intercept form: y - y1 = m(x - x1). The definition of slope involves the distance between points (x1, y1) and (x2, y2) and is represented by (y2 - y1) / (x2 - x1).

Instructions

- 1
  Use the two-point form to convert a linear equation to slope intercept form when the slope and the y-intercept are unknown but two points are given. Use the point slope form but substitute in the definition of a slope for the "m" value to produce the formula y - y1 = ((y2 - y1) / (x2 - x1)) * (x - x1).
- 2
  Find the slope intercept form of a line that includes points (3, 6) and (7, 10). Fill in the two point form with the known information: y - 6 = ((10 - 6) / (7 - 3)) * (x - 3). Simplify, beginning with the slope numbers:y - 6 = (4 / 4) * (x - 3) or y - 6 = 1 * (x - 3). Distribute the 1: y - 6 = x - 3. Add 6 to both sides: y = x + 3.
- 3
  Note that the slope of y = x + 3 is 1 and the y-intercept is 3, or point (0, 3). Find additional points for the graphed line by taking one of the given points and adding the slope by adding 1 to both the x and y values: (3 + 1, 6 + 1) = (4, 7).

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