1) using the line euqation

y = mx +c

where y = price

x = number of cds

substituting y = 490 and x = 80

490 = 80m + c -------(1)

similarly

640 = 200m + c -------(2)

solving the simultaneous equation:

m = 1.25

c = 390

final equation:

y = 1.25x + 390

3) the closest point on the line to the origin creates a line perpendicular which joins the origin and the point on the line closest to the origin to that particular line concerned.

given the equation of the line is 2x + y -2 = 0 → y = -2x + 2---------(1)

using

m1(m2) = -1

the gradient of the other line is 1/2

from y = mx +c

substituting the gradient of the new line

y = 1/2x +c

also since it passes through the origin (0,0)

0 = (1/2)(0) + c

c = 0

equation of new line:

y = x/2 ---------(2)

solving the simultaneous equation (1) and (2)

y = 2/5

x = 4/5