Respuesta :

igoroleshko156

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Answer:  [tex]\textsf{y = 5/7x + 51/7}[/tex]

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Given: [tex]\textsf{Goes through (1, 8) and is parallel to y = 5/7x + 7}[/tex]

Find:  [tex]\textsf{Write an equation that follows that criteria}[/tex]

Solution: We know that our equation is going to parallel to the line that was given therefore the slope would stay the same at 5/7.  We also have a point so we can plug in the values into the point-slope form, distribute, and solve for y.

Plug in the values

  • [tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex]
  • [tex]\textsf{y - 8 = 5/7(x - 1)}[/tex]

Distribute

  • [tex]\textsf{y - 8 = (5/7 * x) + (5/7 * (-1))}[/tex]
  • [tex]\textsf{y - 8 = 5/7x - 5/7}[/tex]

Add 8 to both sides

  • [tex]\textsf{y - 8 + 8 = 5/7x - 5/7 + 8}[/tex]
  • [tex]\textsf{y = 5/7x - 5/7 + 8}[/tex]
  • [tex]\textsf{y = 5/7x + 51/7}[/tex]

Therefore, the final equation that follows the description that was provided in the problem statement is y = 5/7x + 51/7.

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