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Write the equation of the lane that passes through the given point (3,-2) and is (a) parallel and (b) perpendicular to the given line y = 3x-7.

User Mike Ante
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Final answer:

To find an equation parallel to the given line, use the same slope. To find an equation perpendicular to the given line, use the negative reciprocal of its slope.

Step-by-step explanation:

To find an equation parallel to the given line, we know that parallel lines have the same slope. The given line has a slope of 3, so the equation of the parallel line will also have a slope of 3.

Using the point-slope form of a linear equation, we can write the equation as y - (-2) = 3(x - 3). Simplifying this equation gives us y + 2 = 3x - 9.

To find an equation perpendicular to the given line, we need to use the negative reciprocal of its slope.

The negative reciprocal of 3 is -1/3. Using the point-slope form again, the equation of the perpendicular line becomes y - (-2) = -1/3(x - 3). Simplifying this equation gives us y + 2 = -1/3x + 1.

User Josh Boothe
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