Respuesta :

igoroleshko156

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Answer:  [tex]\textsf{y = -1/4x - 4}[/tex]

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Given: [tex]\textsf{Slope = -1/4, Point through = (4, -5)}[/tex]

Find:  [tex]\textsf{Equation for the line that passes through the given point}[/tex]

Solution: In order to get the equation, we need to first use the point-slope form to help us sort out our information and then we solve for y.

Plug in the values

  • [tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex]
  • [tex]\textsf{y - (-5) = -1/4(x - 4)}[/tex]

Simplify and solve for y

  • [tex]\textsf{y + 5 = -1/4(x - 4)}[/tex]
  • [tex]\textsf{y + 5 = -1/4x + 1}[/tex]
  • [tex]\textsf{y + 5 - 5 = -1/4x + 1 - 5}[/tex]
  • [tex]\textsf{y = -1/4x - 4}[/tex]

Therefore, the final answer would be that the equation that has a slope of -1/4 and passes through (4, -5) is y = -1/4x - 4.

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