Final answer:
To find x, set the slope of the given line equal to the negative reciprocal of the slope of the line joining Q to P, and solve for x.
Step-by-step explanation:
To find the value of x, we need to find the point of intersection between the line y=⅔ x - 12 and the line joining the point Q(0, -12) to the point P(x, 0). Since the given line is perpendicular to the line joining Q to P, the slope of the given line will be equal to the negative reciprocal of the slope of the line joining Q to P.
The slope of the line joining Q to P is (0-(-12))/(x-0) = 12/x. Therefore, the slope of the given line is -1/(12/x) = -x/12. Since the slope of the given line is ⅔, we can set up the equation ⅔ = -x/12 and solve for x.
Multiplying both sides of the equation by 12 results in 8 = -x, so x = -8. Therefore, the value of x is -8.