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.