How Do You Find the Point-Slope Form of an Equation?

To find the equation of a line given the slope and a single point, you need to use the point-slope form of y - y1 = m(x - x1). It is almost identical to the slope-intercept form, but you have to find the point for the y-intercept.

  1. Plug in the given values to the point-slope form

    For example, if given the point (3, 5) and a line with a slope of 2, plug in the values into the x1 and y1 terms of the equation. Doing this gives you y - 5 = 2(x - 3).

  2. Simplify the equation on the right side by multiplying

    Multiplying the 2 on the right side by both x and -3 simplifies the equation into y - 5 = 2x - 6.

  3. Cancel out the term on the left

    Add 5 to both sides of the equation. This isolates y and changes the term on the right to 2x -1. Thus, the equation for the line in slope-intercept form is y = 2x - 1. The line crosses the y-axis at (0, -1).

  4. Substitute the original point to check the equation

    The original point is (3, 5). When the numbers are plugged the equation, the equation is 5 = 2(3) -1, which is true.