The line equations are a: , b: , and c: .

The equation of line a: is already adjusted in the slope - intercept form of equation or where m is slope and b is y - intercept.

Therefore slope of line a is 2.

Rewrite the equation of line b: in the slope - intercept form by solving for y.

Subtract 2x from each side.

.

Therefore slope of  line b is .

Rewrite the equation of line c:  in the slope - intercept form by solving for y.

Subtract 4x from each side.

Divide each side by negative 2.

Therefore slope of  line c is 2.

Therefore slopes of line a, line b, and line c are respectively.

The slope line a and line c is same, so these are parallel.

The slope of line a, line b, and line c are negative reciprocals, so line b is perpendicular to the line a and line c.

The line a and line c are parallel and the line b is perpendicular to the line a and line c.