Equations of the solid lines are
Equation of line OA is y = -1/4x
Equation of line OD is y = -3/2x
Equation of line OC is y = 3/2x
Equation of line OB is y = 1/4x
How to derive equation of line
The solid lines are the thick unbroken lines.
Equation of line is give by
y = mx + b
where
m is slope
b is y-intercept
Line OA passes through point (-4,1) and origin (0,0).
slope = 0 - 1/0 - (-4)
m = -1/4
y-intercept = 0(since it pass through the origin)
Equation of line OA is y = -1/4x
For line OD, it passes through (-6,9) and (0,0)
slope = 0-9/0-(-6)
m = -9/6
m = -3/2
y-intercept = 0
Equation of line OD is y = -3/2x
For line OC, it passes through points (6,9) and (0,0)
slope = 9-0/6-0
m = 9/6
m = 3/2
y-intercept = 0
Equation of line OC is y = 3/2x
For line OB, it passes through points (4,1) and (0,0)
slope = 1-0/4-0
m = 1/4
y-intercept = 0
Equation of line OB is y = 1/4x