Final answer:
The equation of the line parallel to y = -2/3x + 5, crossing the x-axis at 6, is y = -2/3x + 4. This matches option B, as parallel lines share the same slope, which is -2/3 in this case.
Step-by-step explanation:
The question asks for the equation in slope-intercept form of the line parallel to the line y = -2/3x + 5 that crosses the x-axis at 6. A parallel line will have the same slope as the line it is parallel to, which in this case is -2/3. Since the line crosses the x-axis at 6, its x-intercept is 6, and this means the y-coordinate at this point is 0 (since all points on the x-axis have a y-coordinate of 0).
To find the slope-intercept form of the equation y = mx + b, where m is the slope and b is the y-intercept, we can use a point that lies on the line and the slope. We know the point (6, 0) lies on our line and the slope is -2/3. Plugging this into the equation, we have 0 = (-2/3)(6) + b. Solving for b yields b = 4. Thus, the equation in slope-intercept form is y = -2/3x + 4, which corresponds to option B.