help please I'm confused

Question

Let O denote the origin,and let A and B be the x-axis and y-axis intercepts of the line y = −bx + c.

1. If the midpoint M of the line segment AB is (3,6), find the values of b and c.
2.  If the triangle AOB has area 4,find c in terms of b.
3. If the midpoint M of AB is such that OM=5,find c in terms of b.

Answer 1

A is the x intercept = (c/b, 0)

B is the y iintercept = (0, c) = the constant term when a linear equation is solved for y

let y=0 to find the x intercept

y=0= -bx + c

x = c/b

M=Midpoint = (3,6)

3 is the average of c/b and 0 = c/2b

6 is the average of c and 0 = c/2

c/2 =6

c =12

c/2b = 12/2b = 6/b = 3

b =6/3 = 2

y=-bx +c

y=-2x +12

b=2, c=12

if area of AOB = 4

then the midpoint is (x,y) where xy=4

and x=y/2 or y^2/2 = 4

y^2 = 8

y =2sqr2

x = sqr2

c=4sqr2

the y intercept is (0,c) = (0,4sqr2)

x intercept =(2sqr2, 0) c/b = 2sqr2

4sqr2/b = 2sqr2

b = 4sqr2/2sqr2 = 2

b=2

y =-2x + 4sqr2

c = 2bsqr2

(assuming no arithmetic error(s) in the above calculations)

if OM=5

5^2 = x^2 +y^2 where (x,y) is the Midpoint

and y=2x

25 = x^2 +4x^2 = 5x^2

x^2 =25/5 = 5

x= sqr5 = c/2b

c =2bsqr5