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    Slope of a Line Equation

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    1. If line / goes through (1,3) and is parallel to the line through (4,3) and (-3,1). find the slope of /.

    2. How do I write the equation y=2/3x-3 in standard form using only integers and a positive coefficient for x.

    3. What is the equation if a line /goes through (-3,-1) and
    (-1,4)?

    4. What is the equation in slope-intercept form) of the line that goes through
    (-1,2) and has slope 4?

    © BrainMass Inc. brainmass.com December 24, 2021, 8:13 pm ad1c9bdddf
    https://brainmass.com/math/graphs-and-functions/slope-line-equation-257675

    SOLUTION This solution is FREE courtesy of BrainMass!

    1. if line / goes through (1,3) and is parallel to the line through (4,3) and (-3,1). find the slope of /.
    Answer -
    Slope of the line passes through two points P(x1 , y1 ) and Q (x2 , y2 ) is given by—
    Slope=
    Here, we have given two end points (4,3) and (-3,1) of a line.
    Let us assume that slope of the line through (4,3) and (-3,1) is m1.
    Thus, slope (m1) of the given line (4,3) and (-3,1) is ---
    Slope (m1) = (1-3)/(-3-4))
    which is equal to—
     -2/ -7
     2/7
     2/7
    m1=2/7
    According to the theorem, two lines are parallel if and only if they have equal slope
    Thus, the line goes through (1,3) and the line through (4,3) and (-3,1) have equal slope.
    Now, assume that the slope of the line goes through (1,3) is m2.
    So, we can write the statement stated above as—
    m1 = m2 = 2/7
    Thus, the slope of the line goes through (1,3) is 2/7

    2. how do i write the equation y=2/3x-3 in standard form using only integers and a positive coefficient for x.
    Answer -
    Standard form of equation is
    Ax+ By = C, where A,B and C are constants.
    Now, y=2x/3-3 can be written as—
    -3=y
    By taking LCM (3) on the left hand side, we get—
    =y
    This equation can be further written in simplest form as---
    2x-9=3y
    In the standard form, it can be written as—
    2x-3y=9

    3. what is the equation if a line /goes through (-3,-1) and
    (-1,4)?
    Answer -
    Any line passing through the two points P(x1 , y1 ) and Q (x2 , y2 ) is given by:-

    (y-y1 )= * (x - x1)

    In your question (x1 , y1 ) is (-3 , -1) and (x2 , y2 ) is (-1 , 4).

    The equation of the line passing through these points is

    (y - (-1)) = * (x-(-3))
    or (y +1) = * (x+3)
    or (y +1) = * (x+3)
    Cross Multiplying we have -

    2y + 2 = 5x + 15

    or 5x - 2y + 13 = 0 is the required equation.

    4. what is the equation in slope-intercept form) of the line that goes through
    (-1,2) and has slope 4?
    Answer -
    The slope-intercept form is given by,
    y = mx + c
    where, m is the slope of the line and c is the y-intercept.
    or the other way of writing it is -
    (y-y1 )= m (x - x1)
    Where, m is the slope of the line.
    Now we have (x1, y1) = (-1, 2) and slope = 4.
    Using the above slope-intercept form, we have -
    (y - 2) = 4(x - (-1))
    (y - 2) = 4(x + 1)
    y - 2 = 4x + 4
    Adding 2 on both sides we have -
    y - 2 + 2 = 4x + 4 + 2
    y = 4x + 6.
    This is the equation in the slope intercept form.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 8:13 pm ad1c9bdddf>
    https://brainmass.com/math/graphs-and-functions/slope-line-equation-257675

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