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Find an equation for the line that passes through the point P(-5,-3) and is parallel to the line
7x + 4y
10. Use exact values.

Sagot :

igoroleshko156

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Answer:  [tex]\textsf{y = -1.75x - 11.75}[/tex]

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Given:  [tex]\textsf{Goes through (-5, -3) and parallel to 7x + 4y = 10}[/tex]

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

Solution: We need to first solve for y in the equation that was provided so we can determine the slope.  Then we plug in the values into the point-slope form, distribute, simplify, and solve for y to get our final equation.

Subtract 7x from both sides

  • [tex]\textsf{7x - 7x + 4y = 10 - 7x}[/tex]
  • [tex]\textsf{4y = 10 - 7x}[/tex]

Divide both sides by 4

  • [tex]\textsf{4y/4 = (10 - 7x)/4}[/tex]
  • [tex]\textsf{y = (10 - 7x)/4}[/tex]
  • [tex]\textsf{y = 10/4 - 7x/4}[/tex]
  • [tex]\textsf{y = 2.5 - 1.75x}[/tex]

Plug in the values

  • [tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex]
  • [tex]\textsf{y - (-3) = -1.75(x - (-5))}[/tex]

Simplify and distribute

  • [tex]\textsf{y + 3 = -1.75(x + 5)}[/tex]
  • [tex]\textsf{y + 3 = (-1.75 * x) + (-1.75 * 5)}[/tex]
  • [tex]\textsf{y + 3 = -1.75x - 8.75}[/tex]

Subtract 3 from both sides

  • [tex]\textsf{y + 3 - 3 = -1.75x - 8.75 - 3}[/tex]
  • [tex]\textsf{y = -1.75x - 8.75 - 3}[/tex]
  • [tex]\textsf{y = -1.75x - 11.75}[/tex]

Therefore, the final equation in slope-intercept form that follows the information that was provided is y = -1.75x - 11.75

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