# For y = -2x - 7 find the equation of the line parallel to it and perpendicular to it that passes through (1, -2). Graph the lines.

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The equation of the line parallel to y = -2x - 7 has to be determined that passes through (1, -2)

The slope of two parallel lines is the same. As the line parallel to y = -2x - 7 passes through (1, -2), the equation of the line is:

(y + 2)/(x - 1) = -2

=> y + 2 = 2 - 2x

=> 2x + y = 0

The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the line. The slope of y = -2x - 7 is -2. The slope of a line perpendicular to this is 1/2.

As the line passes through (1, -2), the equation is (y + 2)/(x - 1) = 1/2

=> 2y + 4 = x - 1

=> x - 2y - 5 = 0

The graph of the parallel line (red) and perpendicular line (green) is: