Question

Find the equation of the line through the point (2, 5) that cuts off the least area from the first quadrant. Give your answer using the form below.

y − A = B(x − C)

Answer 1

lets say the equation is
y = mx+b
m is the slope, b is the y intercept.
the line will cut a triangular region in the first quadrant.
its area is 1/2 base times height.
the height is the y intercept
and the base is y intercept divided by slope
so the area is b^2/2m

Answer 2

now, we know that the line passes through (2,5)
so
5 = 2m+b,
or 2m = 5-b
substitute that in the area (call it A)
A = b^2/5-b
to find the least area, differentiate the area with respect to the height and equate it to 0
dA/db = 0
find b
use that to find m
you have the equation of the line
manipulate that to get it in the form that the problem asks for.

Answer 3

got it?