I had 4 questions, i wrote em up in photoshop i thought it would be easier.
1.
2.
3.
4.
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