Final answer:
In Quadrant III, the line through the origin parallel to 7x-2y=-6 can be written as y = (7/2)x.
Step-by-step explanation:
In Quadrant III, we know that the x-coordinate is negative and the y-coordinate is negative. So, for the line to pass through the origin and be parallel to the line 7x-2y=-6, the slope of the line must be the same.
The given line equation can be rewritten in slope-intercept form: y = (7/2)x + 3. The slope of this line is 7/2, so the line through the origin parallel to this line will also have a slope of 7/2.
Therefore, the equation of the line through the origin parallel to 7x-2y=-6 in Quadrant III can be written as y = (7/2)x.