Find the equation of a line that is parallel to y = -2x + 3, and perpendicular to it passing through (-2, -3). Graph the lines.

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We have to determine the line parallel to y = -2x + 3, passing through (-2, -3). Two perpendicular lines have the same slope. The slope of y = -2x + 3 is -2. The required line is of the form y = -2x + C and passes through (-2, -3)

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We have to determine the line parallel to y = -2x + 3, passing through (-2, -3). Two perpendicular lines have the same slope. The slope of y = -2x + 3 is -2. The required line is of the form y = -2x + C and passes through (-2, -3)

=> -3 = -2*-2 + C

=> C = -7

The required parallel line is y = -2x - 7

The line perpendicular to y = -2x + 3 has a slope (1/2). It is of the form y = (1/2)x + C. As it passes through (-2, -3)

=> -3 = (1/2)*-2 + C

=> C = -2

The required perpendicular line is y = x/2 - 2

The graphs of lines are:

 

The required parallel line is y = -2x - 7 and the required perpendicular line is y = x/2 - 2

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