Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

find the value of r so the line passes that through (-5,2) and (3,r) has a slope of -1/2?

7 Answers

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  • 2 months ago

    The typical equation of a line is: y = mx + y₀ → where m: slope and where y₀: y-intercept

    y = mx + y₀ ← this is the equation of the line (ℓ)

    The line has a slope of (- 1/2), so you can say that: m = - 1/2

    y = - (1/2).x + y₀

    The line passes through (- 5 ; 2), so these coordinates must verify the equation of the line.

    y = - (1/2).x + y₀

    y₀ = y + (1/2).x → you substitute x and y by the coordinates of the point (- 5 ; 2)

    y₀ = 2 + [(1/2) * - 5]

    y₀ = 2 - (5/2)

    y₀ = - 1/2

    Recall the equation of the line:

    y = - (1/2).x + y₀ → we've just seen that: y₀ = - 1/2

    y = - (1/2).x - (1/2) → to go further

    y = (- x - 1)/2

    2y = - x - 1

    x + 2y = - 1 ← this is the equation of the line (ℓ)

    x + 2y = - 1 → as the point (3 ; r) belongs to the line, its coordinates verify the equation

    3 + 2r = - 1

    2r = - 4

    r = - 2

  • ?
    Lv 7
    2 months ago

    (r-2)/(3-(-5))=-1/2

    =>

    r-2=8(-1/2)

    =>

    r-2=-4

    =>

    r=-2

  • 2 months ago

    Let's apply the slope formula to solve for r..

    .........y₂ - y₁

    m = --------------

    .........x₂ - x₁₂

    ............r - 2

    -1/2 = ---------

    ............3 - (-5)

    ..............r - 2

    - 1/2 = ------------

    ................8

    - 4 = r - 2

    - 4 + 2 = r

    r = - 2 Answer//

  • 2 months ago

     The value of r so that the line passes through (-5, 2) and (3, r) 

     and has a slope of -1/2:

     (-5, 2), (3, r) 

     m = -1/2

     (2 -  r) / (-5 - 3) = -1/2

     2(2 - r) = -1(-5 - 3)

     4 - 2r = 8

     2r = -4

     r = -2

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  • Jeremy
    Lv 6
    2 months ago

    -1/2 = (r - 2)/(3 - (-5)) ===> -1/2 = (r - 2)/(3 + 5) ===> -1/2 = (r - 2)/8 ===>

    ===> -4 = r - 2 ===> -4 + 2 = r ===> r = -2 (ANSWER)

  • ?
    Lv 7
    2 months ago

    The value of r = -2 because the slope is (2--2)/(-5-3) = -1/2 and the points are (-5, 2) and (3, -2)

  • 2 months ago

    The slope is a change in y over the change in x.  So we can set up this equation:

    m = (y₁ - y₂) / (x₁ - x₂)

    Using the two points: (-5, 2) and (3, r) for the x's and y's and m = -1/2, we can substitute this into the equation and solve for the unknown:

    -1/2 = (2 - r) / (-5 - 3)

    -1/2 = (2 - r) / (-8)

    4 = 2 - r

    2 = -r

    -2 = r

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