What is the equation of the line perpendicular to 2x – 3y = 13 that passes through the point (–6, 5)? will give

y = (-3/2) - 4

Step-by-step explanation

2x - 3y = 13, when solved for -3y, results in -3y = -2x + 13.  Then y = (2/3)x + C.  Any line perpendicular to this y = (2/3)x + C has the slope which is the negative reciprocal of (2/3); that slope is -3/2.

Thus, the desired equation has the form y = (-3/2)x + b.  

Subbing 5 for y and -6 for x, we get:  5 = (-3/2)(-6) + b, or 5 = 9 + b.  Thus, b = -4, and so the equation of the line perpendicular to 2x - 3y = 13 is y = (-3/2) - 4.

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