Write an Equation Given Two Points

Key Questions

  • Slope Formula

    The slope formula of the line passing through the points #(x_1,y_1)# and #(x_2,y_2)# can be found by:

    #m={y_2-y_1}/{x_2-x_1}#

    So to find the slope of a line segment joining the points ( 2, - 5) and (- 2, 4).

    First, label the points as #x_1# = 2, #y_1# = - 5, #x_2# = -2 and #y_2# = 4

    #m={y_2-y_1}/{x_2-x_1}# = #{4- -5}/{-2- 2}# = #{9}/{-4}# = #{-9}/{4}#

    So, the slope (#m#) = -9/4.

  • No, it does not as long as the point is on the line. You will end up with the same value for the #y#-intercept.


    I hope that this was helpful.

  • If the slope of a line is undefined, then the line is a vertical line, so it cannot be written in slope-intercept form, but it can be written in the form: #x=a#, where #a# is a constant.


    Example

    If the line has an undefined slope and passes through the point #(2,3)#, then the equation of the line is #x=2#.


    I hope that this was helpful.

  • Answer:

    Use the differences in the y and x values to find the slope then substitute the values of one point into the equation to find b the y intercept.

    Explanation:

    Slope = #( y_1-y_2)/(x_1-x_2)=m#

    By putting the x and y values for the two points into the slope equation the value for m can be found.

    The equation of a line in the slope intercept form is

    # y = mx +b #

    After finding m using the slope equation substitute one set of point values for y and x. This leaves b as the only unknown. Slope the resulting equation for b.

Questions