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Find the equation of the line parallel to y = -1/2 - 4 and goes through the point (-2,-5)

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Answer:

The equation of the line is y = - 1/2 x - 6

Explanation:

The equations of parallel lines have the same slopes and different y-intercepts

The form of the linear equation is y = m x + b, where

  • m is the slope of the line
  • b is the y-intercept (value y at x = 0)
  • To find b substitute x and y in the equation by the coordinates of a point on the line

∵ The given equation is y = -1/2 x - 4

→ By comparing it by the form of the equation above

∴ m = -1/2

∵ Parallel lines have the same slope

The slope of the line = -1/2

→ Substitute it in the form of the equation above

y = - 1/2 x + b

∵ The line passes through the point (-2, -5)

→ To find b substitute x by -2 and y by -5

∴ -5 = -1/2 (-2) + b

∴ -5 = 1 + b

→ Subtract 1 from both sides

∴ -5 - 1 = 1 - 1 + b

-6 = b

→ Substitute the value of b in the equation above

∴ y = - 1/2 x + (-6)

y = - 1/2 x - 6

The equation of the line is y = - 1/2 x - 6

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