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An equation for a line perpendicular to p(t) = 3t 4 and passing through the point (3,1)

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Final answer:

To find the equation for a line perpendicular to p(t) = 3t + 4 and passing through the point (3,1), the slope of the perpendicular line is -1/3. Using the point-slope form of a line, the equation of the perpendicular line is y = (-1/3)x + 2.

Step-by-step explanation:

To find the equation for a line perpendicular to p(t) = 3t + 4 and passing through the point (3,1), we first need to determine the slope of the given line. The given line is in the form y = mx + b, where m represents the slope. Comparing it with the equation p(t) = 3t + 4, we can see that the slope is 3.

The slope of a line perpendicular to another line is the negative reciprocal of the original slope. So, the slope of the perpendicular line will be -1/3. Now, using the point-slope form of a line, we can write the equation of the perpendicular line as y - 1 = (-1/3)(x - 3).

Simplifying the equation, we get y = (-1/3)x + 2.

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