Question:

<p><strong>Step 1: Identify the rectangle's properties.</strong><br>The rectangle has corners at (0, 0), (4, 0), (4, 2), and (0, 2).<br>Width = 4, Height = 2<br>Area = 4 × 2 = 8</p><p><strong>Step 2: Find the center of the rectangle.</strong><br>The center (or centroid) of the rectangle is at the midpoint of the diagonal:<br>Center = ((0+4)/2, (0+2)/2) = (2, 1)</p><p><strong>Step 3: Determine the equation of the line.</strong><br>The required line is parallel to y = 3x, so it has slope m = 3.<br>A line that bisects the area of a rectangle must pass through its center.<br>Using point-slope form with point (2, 1) and slope 3:<br>y - 1 = 3(x - 2)<br>y - 1 = 3x - 6<br>y = 3x - 5</p><p><strong>Step 4: Find the y-intercept.</strong><br>Set x = 0 in the equation y = 3x - 5:<br>y = 3(0) - 5 = -5<br>The y-intercept is at (0, -5).</p><p><strong>Verification:</strong> The line y = 3x - 5 passes through (2, 1): y = 3(2) - 5 = 1 ✓<br>This line divides the rectangle into two equal areas of 4 square units each.</p><p><strong>∴ Answer: D</strong></p>