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Point slope formula





The point-slope formula is used in coordinate geometry to find the equation of a line when you know the slope of the line and the coordinates of a point on the line. This formula is especially useful for writing the equation of a line in a quick and straightforward manner.

Point-Slope Formula

The point-slope formula is expressed as y – y1 = m(x – x1), where:

  • ‘m’ is the slope of the line.
  • (x1, y1) are the coordinates of a known point on the line.
  • (x, y) are the coordinates of any other point on the line.

How to Use the Point-Slope Formula

  1. Start with the slope of the line and the coordinates of a known point on the line.
  2. Substitute the slope (m) and the coordinates of the known point (x1, y1) into the formula.
  3. Rearrange the formula to solve for y, if needed, to get the equation in slope-intercept form (y = mx + b).

Example 1

Write the equation of the line with a slope of 2 that passes through the point (3, 4).

Using the point-slope formula: y – 4 = 2(x – 3). This can be simplified to y = 2x – 2.

Example 2

Write the equation of the line with a slope of -1 that passes through the point (-2, 5).

Using the point-slope formula: y – 5 = -1(x + 2). This can be simplified to y = -x + 3.


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