Write an Equation Given the Slope and a Point

Key Questions

  • What do the variables "m" and "b" represent?

    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.

    AJ Speller · 3 · Sep 30 2014
  • How do you write an equation in slope intercept form given a slope and a x-intercept?

    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.

    MeneerNask · 1 · Dec 22 2014
  • When writing an equation of a line, if I know more than one point, does it matter which one I choose?

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

    I hope that this was helpful.

    Wataru · 1 · Oct 29 2014
  • How do you write an equation in slope intercept form given the slope and a point?

    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 = 3/4x + 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.

    BRIAN M. · 1 · Oct 24 2014

Questions

Forms of Linear Equations