Mathematics

Question

Find the equation of the line perpendicular to x−5y=15 that passes through the point (−2,5).

2 Answer

  • 1. Solve the given equation for y.

    x - 5y = 15

    -5y = -x + 15

    y = (-x + 15)/-5

    y = (x/5) - 3

    y = (1/5)(x) - 3

    The slope is 1/5. See it?

    The equation we are looking for has a slope which is the negative inverse of the slope in the equation we just solved for y.

    The slope for the equation we want is -5 which is the negative inverse of 1/5. Undetstand?

    We have the slope of the new equation and one point is given.

    Plot BOTH into the point-slope formula and solve for y. To solve for a variable means to isolate the variable ALONE on one side of the equation.

    y - y_1 = m(x - x_1)...This is the point-slope formula. Our given point is (5,-2)

    y - 5 = -5(x - (-2))

    y - 5 = -5(x + 2)

    We now solve for y and that's it.

    y - 5 = -5x - 10

    y = -5x - 10 + 5

    The equation we want is y = -5x - 5.
  • 1. Solve the given equation for y.


    x - 5y = 15


    -5y = -x + 15


    y = (-x + 15)/-5


    y = (x/5) - 3


    y = (1/5)(x) - 3


    The slope is 1/5. See it?


    The equation we are looking for has a slope which is the negative inverse of the slope in the equation we just solved for y.


    The slope for the equation we want is -5 which is the negative inverse of 1/5. Undetstand?


    We have the slope of the new equation and one point is given.


    Plot BOTH into the point-slope formula and solve for y. To solve for a variable means to isolate the variable ALONE on one side of the equation.


    y - y_1 = m(x - x_1)...This is the point-slope formula. Our given point is (5,-2)


    y - 5 = -5(x - (-2))


    y - 5 = -5(x + 2)


    We now solve for y and that's it.


    y - 5 = -5x - 10


    y = -5x - 10 + 5


    The equation we want is y = -5x - 5.


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