Final answer:
To find the value of r, use the formula for slope and set up an equation based on the given points and slope. Therefore the correct answer is r = 5.
Step-by-step explanation:
The given points are (r, -6) and (3, -3) with a slope of -3/2. To find the value of r, we can use the formula for slope, which is the change in y divided by the change in x. So, (-3 - (-6))/(3 - r) = -3/2. Simplifying this equation, we get (-3 + 6)/(3 - r) = -3/2. Combining like terms, we have 3/(3 - r) = -3/2.
Cross-multiplying, we get 6 = -9 + 3r. Rearranging the equation, we have 3r = 6 + 9, which gives us 3r = 15. Finally, dividing both sides by 3, we find that r = 5.