Write an Equation Given the Slope and a Point

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Point Slope Form Introduction

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Key Questions

  • Slope Intercept form is y = mx + b, where
    m = the slope and b = the y- intercept.

    Slope is determined by formula

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

    if you had the coordinates of two points on the line.

    #(x_1,y_1) (x_2,y_2)#

    b is the point at which the line will cross (intercept) the y-axis.

    If a problem asked for the slope intercept form and provides a slope and a single point on the line you could find the equation with two different methods.

    What is the slope intercept equation of a line with a slope of m = 3/4 and a point on the line of (4 , 5)?

    The first method is to us the slope-intercept equation and plug in values to solve for b.

    5 = #3/4#(4) + b (simplify the fraction)

    5 = 3 + b (isolate b)

    5 - 3 = b (simplify)

    b = 2

    The slope-intecept equation would be y = #3/4#x + 2

    The second method is to use the point-slope formula

    #(y - y_1) = m(x - x_1)#

    Plug in the information and simplify for the equation.

    #(y - 5) = 3/4(x - 4)# (distribute the slope)

    #(y - 5) = 3/4x - 3# (isolate y)

    #y = 3/4x - 3 + 5# (simplify)

    #y = 3/4x + 2# is the slope-intercept equation.

  • The slope intercept formula is, #y=mx+b#

    where #m# is the slope
    where #b# is the #y#-intercept

    The slope is the change in y over the change in x. This is commonly known as the #(rise)/(run)#. This is also shown as the #(Deltay)/(Deltax)#. If you have any 2 points on the line than you can also use the formula #(y_2-y_1)/(x_2-x_1)#.

    The y-intercept is where the line touches or intersects the #y#-axis. If the #x# coordinate is zero you can find out what the y-intercept is.

  • What is x-intercept? It is such an argument (x-value) where y-value equals 0. In equations you would tell that it is root of the equation.

    In general formula #y = mx+b# you insert known information, where #m# is a slope (or gradient) and #b# is free-term (or y-intercept - such an value where function cuts y-axis, so point (0, b) ).

    Let us take example. You are given slope - it is 2. And you know that your x-intercept is equal 3. Therefore, you know that when #x = 3#, #y=0#.

    Let us use that information. You know that you may write every linear function like that: #y = mx+b#.
    Let us insert values: #0 = 2*3+b#
    Our unknown is #b#, free term. Let us isolate it:
    #b=-6#.
    And after all, we must insert our #b# value back into equation: #y = 2x - 6#.

  • No, it does not matter since you will end up with an equivalent equation.


    I hope that this was helpful.

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