Question

Write the function AG(X) representing the area of the garden in terms of x.

Answer 1

The area of this rectangle is x*y. But, this problem requires that you represent the variable "y" in terms of "x" only.

A hint here is that the variable "y" represent a point on the line that connects the end points (0,b) and (a,0).

The first step to solve this problem is to get the expression of this line.

The slope of this line is:   m = (0 - b)/(a - 0) = -b/a

Because the point (x,y) is on this line we have:   y - b = m(x - 0)

                                                                      y = (-b/a)x + b

Solution: Area of the rectangle = x*y = x*((-b/a)x + b) = (-b/a)x2 +bx