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Select the correct answer. What is the slope-intercept form of the equation of a line that passes through (5, -4) and has a slope of `3/4`? A. `y = -(3)/(4) x -(1)/(4)` B. `y = 3/4 x +(1)/(4)` C. `y = 3/4 x -(31)/(4)` D. `y = 3/4 x +(31)/(4)`

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igoroleshko156

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Answer:  [tex]\textsf{y = 3/4x - 7.75}[/tex]

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Given:  [tex]\textsf{Passes through (5, -4) with a slope of 3/4}[/tex]

Find:  [tex]\textsf{The equation in slope-intercept form}[/tex]

Solution:  In order to determine the equation we need to first plug the values into the point-slope form, simplify, distribute, and solve for y to get our final result.

Plug in the values

  • [tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex]
  • [tex]\textsf{y - (-4) = 3/4(x - 5)}[/tex]

Simplify the expression and distribute

  • [tex]\textsf{y + 4 = 3/4(x - 5)}[/tex]
  • [tex]\textsf{y + 4 = (3/4 * x) + (3/4 * -5)}[/tex]
  • [tex]\textsf{y + 4 = 3/4x - 3.75}[/tex]

Subtract 4 from both sides

  • [tex]\textsf{y + 4 - 4 = 3/4x - 3.75 - 4}[/tex]
  • [tex]\textsf{y = 3/4x - 3.75 - 4}[/tex]
  • [tex]\textsf{y = 3/4x - 7.75}[/tex]

The equation in slope-intercept form that follows the information that was provided is y = 3/4x - 7.75

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