Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

Points S(4, 10) and T(-2, -8)are on a line.Which equation represents a line that is perpendicular to this line and has the same y-intercept?

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  • fcas80
    Lv 7
    2 months ago

    The line ST has slope (10 - - 8)/(4 - - 2) = 3.  The equation is y - 10 = 3(x - 4), or y = 3x +2.  It y-intercept is 2.  A line perpendicular to it has slope -1/3.  If that line also has the same y-intercept, then that line is y = -1/3(x - 6).

  • 2 months ago

    You want the equation of a line that is perpendicular to the line represented by the two points that has the same y-intercept. 

    First, we need to put the original line into slope-intercept form to know its slope and y-intercept.  Starting with the general equation:

    y = mx + b

    Substitute the "x" and "y" values of the known points into the equation to get a system of two equations and two unknowns that we can solve:

    (4, 10) and (-2, -8)

    10 = m(4) + b and -8 = m(-2) + b

    Solve both for b in terms of m:

    10 = 4m + b and -8 = -2m + b

    10 - 4m = b and -8 + 2m = b

    Two expressions are each equal to "b", so both expressions are also equal to each other.  Solve for m:

    10 - 4m = -8 + 2m

    -6m = -18

    m = 3

    Now that we know "m", solve for "b":

    b = 10 - 4m

    b = 10 - 4(3)

    b = 10 - 12

    b = -2

    So the slope of the original line is 3 and the intercept is -2.

    The perpendicular line will have a negative-reciprocal slope to the original.  So that slope is -1/3.  The intercepts are to be the same, so the equation of the second line is:

    y = (-1/3)x - 2

  • 2 months ago

       First to post  ...... Here are the hints.. you do the work....

    ****  it's sad  so many do all the work for you, instead of letting you do it for yourself... you won't learn that way  ****

    Anyway, choose a Best Answer, but NOT because they Gave you the Answer...

    1.  find  eqn of line thru S,T   use  y - y1 = m ( x - x1)

       I used  x1 = 4    y1 = 10

    2.  rewrite  eqn in  slope intercept  form... y = mx + b

    3.  the perpendicular  has  the same y intercept... b,  only  m is different.

    4.  Now  what do you remember about slopes for a perpendicular  ?  it is  negative  reciprocal of the other lines  slope.

    5. Now you have  y = mx + b  for the perpendicular  line.

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