Answer: D. $y=-\dfrac{x}{3}+7$

Explanation:1. Recall the point-slope form of a linear equation: The point-slope form is $y - y\_1 = m(x - x\_1)$, where $m$ is the slope and $(x\_1, y\_1)$ is a point on the line.

2. Substitute the given slope and point into the point-slope form: Given slope $m = -\dfrac{1}{3}$ and point $(x\_1, y\_1) = (9, 4)$. $y - 4 = -\dfrac{1}{3}(x - 9)$

3. Convert the equation to slope-intercept form ($y = mx + b$): Distribute the slope on the right side: $y - 4 = -\dfrac{1}{3}x - \dfrac{1}{3}(-9)$ $y - 4 = -\dfrac{1}{3}x + \dfrac{9}{3}$ $y - 4 = -\dfrac{1}{3}x + 3$ Add 4 to both sides to isolate y: $y = -\dfrac{1}{3}x + 3 + 4$ $y = -\dfrac{1}{3}x + 7$

4. Compare with the given options: The equation we derived is $y = -\dfrac{1}{3}x + 7$. This matches option [D]: $y=-\dfrac{x}{3}+7$.

5. Alternative method: Check options Option [A]: Slope is 7, not $-\dfrac{1}{3}$. Incorrect. Option [B]: Slope is 9, not $-\dfrac{1}{3}$. Incorrect. Option [C]: Slope is $-\dfrac{1}{3}$. Check if (9,4) satisfies it: $4 = -\dfrac{9}{3} + 4 \Rightarrow 4 = -3 + 4 \Rightarrow 4 = 1$. False. Incorrect. Option [D]: Slope is $-\dfrac{1}{3}$. Check if (9,4) satisfies it: $4 = -\dfrac{9}{3} + 7 \Rightarrow 4 = -3 + 7 \Rightarrow 4 = 4$. True. Correct.

6. Conclusion: The equation that defines line t is $y=-\dfrac{x}{3}+7$.