Final answer:
To find the length of PT, substitute the given values for TQ and solve for x. Use the formula PT = 3x + 9 and substitute the value of x into the equation to find PT.
Step-by-step explanation:
To find the length of PT, we need to substitute the given values for TQ and solve for x. The formula for the length of a line segment is PT = 3x + 9. We are given that TQ = 8x - 6. Setting TQ equal to 0 and solving for x gives us x = 3/8. Substituting this value into the formula for PT gives PT = 3(3/8) + 9, which simplifies to PT = 2.25 + 9, and finally PT = 11.25.