Consider the line that passes through the point P(4, - 2) and is parallel to the line - 3x - 4y = 2 Write the point-slope equation of the line. Use exact values.

9514 1404 393

  y +2 = -3/4(x -4)

Step-by-step explanation:

A line parallel to ...

  ax +by = c

through point (h, k) can have the equation ...

  a(x -h) +b(y -k) = 0

It is pretty simple to put this into point-slope form:

  b(y -k) = -a(x -h) . . . . . subtract the x-term

  y -k = (-a/b)(x -h) . . . . divide by b

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We have ...

  a = -3, b = -4, (h, k) = (4, -2)

so the point-slope form equation is ...

  y -(-2) = (-(-3)/(-4))(x -4)

  y +2 = -3/4(x -4)

both equations and proportions are better.