Question: Choose the graph that correctly plots the point \((-6, 3\pi)\). A. [Graph A] B. [Graph B] C…

Choose the graph that correctly plots the point \((-6, 3\pi)\).

A. [Graph A]

B. [Graph B]

C. [Graph C]

D. [Graph D]

Solution

To find the graph that correctly plots the point \((-6, 3\pi)\): 1. Identify the coordinates: \((-6, 3\pi)\). This means the x-coordinate is \(-6\) and the y-coordinate is \(3\pi\). 2. Check the x-coordinate: The point should be 6 units to the left of the origin on the x-axis because the x-coordinate is negative. 3. Check the y-coordinate: The point should be approximately \(3 \times 3.14 = 9.42\) units above the origin since \(3\pi\) is positive. Looking at the graphs: - Option A: Point is on the negative x-axis. - Option B: Point looks to be negative in the x-direction and positive in the y-direction. - Option C: Point is on the positive y-axis. - Option D: Point is on the positive x-axis. The correct choice is B, as it plots the point \((-6, 3\pi)\) in the correct quadrant.