Line p passes through (8, -6) and is perpendicular to the line 2x + y = -7.

the slope of line p is .
the equation of line p is y = 1/2x +

y = (1/2)x - 10

Step-by-step explanation:

First we determine the slope of new line p.  This slope is the negative reciprocal of the given line 2x + y = -7.  Solving 2x + y = -7 for y is the easiest way in which to determine the slope of this line.  y = -2x - 7 has the slope -2.

The negative reciprocal of this slope -2 is +1/2.

Given that line p passes through (8, -6) and that the slope of p is 1/2, we can easily solve for the y-intercept, b, of p:

Starting with y = mx + b, we get -6 = (1/2)(8) + b, or -6 = 4 + b.  

Then b = -10, and the equation of line p is y = (1/2)x - 10.

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