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  y = 2/3x -20/3

Step-by-step explanation:

The perpendicular line will have a slope that is the opposite of the reciprocal of the slope of the given line:

  -1/(-3/2) = 2/3

You can use the point-slope form to write the equation of that perpendicular line.

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

  y +2 = 2/3(x -7) . . . . . the equation of the perpendicular line

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This can be put into slope-intercept form by solving for y and simplifying.

  y +2 = 2/3x -14/3

  y = 2/3x -20/3

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step-by-step explanation:

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