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How to Change From a Point Slope to a Slope Intercept

The point-slope and slope-intercept forms of linear equations provide different ways of expressing the same line. The point-slope form is useful when you know the coordinates of one point and the slope of the line. The slope-intercept form is often more convenient when you know the slope and the place where the line crosses the y-axis. However, because both of these equations express the same line, you can switch from one to another according to your preference.

Instructions

- 1
  Substitute the values of x1 and y1 in the point-slope formula y - y1 = m(x - x1), for x and y in the slope-intercept formula y = mx + b.
  
  For example, if the point-slope formula is y - 7 = 2(x - 1), the slope-intercept formula would be 7 = m(1) + b.
- 2
  Substitute the value of m in the point-slope formula for m in the slope-intercept formula.
  
  Since m equals 2 in the point-slope formula, the slope-intercept formula would be 7 = 2(1) + b.
- 3
  Solve the slope-intercept formula for the y-intercept, or b.
  
  Since 7 = 2 + b, b = 5.
- 4
  Insert the value of b into the formula.
  
  The formula now looks like this: 7 = 2(1) + 5.
- 5
  Replace the numerical values of x and y with variables so that the formula can apply to any point on the line, but leave the values of m and b in place.
  
  The slope-intercept form of the line is y = 2x + 5.

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