Final answer:
None of the provided options for the equation of the line through the point (3, 5) that cuts off the least area from the first quadrant is correct. The correct equation should be y = (5/3)x, where (5/3) is the slope computed from the points (0, 0) and (3, 5), resulting in a line that passes through the origin, cutting off the least possible area.
Step-by-step explanation:
The student's question asks for the equation of the line that passes through the point (3, 5) and cuts off the least area in the first quadrant. To minimize the area in the first quadrant, the line must also pass through the origin (0, 0). This is because any non-vertical line that does not pass through the origin will form a triangle with a larger area.
Using the two points (0, 0) and (3, 5), we can find the slope of the desired line through the usual formula for slope, m = (y2 - y1) / (x2 - x1). Substituting the points gives us m = (5 - 0) / (3 - 0) = 5/3. To find the equation of a line, we use the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Since our line passes through the origin, the y-intercept b is 0. Thus, our equation becomes y = (5/3)x.
Comparing this result with the provided options, none of them matches exactly, suggesting there may have been a typo in the question or the provided options. If the options represent different questions, each option represents a line with a unique slope and y-intercept, and the line equation y = mx + b reflects the general form of a linear equation.