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find the value of K so that the line through the points (4,-3) and(k,7) is parallel to the line with the equation 4x+6y=10

User Adam Beck
by
7.8k points

1 Answer

4 votes

Answer:

-8

Explanation:

Convert the equation from standard form into slope-intercept form by....

  • Moving the variable to the right-hand side and change its sign: 6y = 10 - 4x
  • Divide both sides of the equation by 6 : y=
    (5)/(3)-
    (2)/(3)x
  • Use the commutavie property to reoder the terms : y= -
    (2)/(3)x +
    (5)/(3)

(Parallel lines have the same slope.. so the slope = -
(2)/(3))

Create and equation using the slope and the point (k,7)

  • Make the equation : 7 = -
    (2)/(3)(k) +
    (5)/(3)
  • Multiply both sides of the equation by 3 : 21 = -2k + 5
  • Move the varable to the left-hand side and change its sign: 2k + 21 = 5
  • Move the constant to the right-hand side and change its sign: 2k + 5 - 21
  • Calculate the difference: 2k = -16
  • Divide both sides of the equation by 2 : k= -8

Solution : k = -8

User Akyegane
by
7.9k points

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