Slope-Intercept Form

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Key Questions

  • Answer:

    #y = mx + b#

    Where:
    #m# is the slope of the line.
    #b# is the y-intercept of the line.

    Explanation:

    Consider #y = x#

    graph{y=x [-10, 10, -5, 5]}

    In this equation, the coefficient to #x# is 1 and our y-intercept is 0.

    We could think of that equation as looking like:

    #y = 1x + 0#

    Notice that the graphed line has a "rise-over-run" of #1/1# which is just 1 and the line passing through the y-axis at #y=0#

  • Answer:

    #m# is the slope, while #b# is the y-intercept.

    Explanation:

    Any linear equation has the form of

    #y=mx+b#

    • #m# is the slope of the equation

    • #b# is the y-intercept

    The slope of the line, #m#, is found by

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

    where #(x_1,y_1)# and #(x_2,y_2)# are the coordinates of any two points in the line.

    The y-intercept, #b#, is found by plugging in #x=0# into the equation, which results in #y=b#, and therefore is the y-intercept.

    In some cases, if the equation is already arranged for you nicely, like #y=3x+5#, we can easily find the y-intercept for this line, which is #5#.

    Other times, the equation might not be arranged nicely, with cases such as #1/2x+3y=5#, in which we solve for the y-intercept:

    #1/2x+3y=4#

    #3y=4-1/2x#

    #y=(-1/2x+4)/3#

    #y=-1/6x+4/3#

    So, the y-intercept of this line is #4/3#.

  • The #y#-intercept #b# can be found by reading the #y#-axis where the graph hits the y-axis, and the slope #m# can be found by finding any two distinct points #(x_1,y_1)# and #(x_2,y_2)# on the graph, and using the slope formula below.

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


    I hope that this was helpful.

Questions