State whether the lines represented by the equations 2y-x=1 and y + 4= -1/2(x-2) are parallel, perpendicular or neither

Answer 1

If any equation equation in the form of y=mx+c this is represent straight line where m is slop of that line and c is intercept of y axis so ....if two lines are parallal their slops are eqall m¹=m² and they are perpendicular multiplication of slops is -1

2y-x=1

y=(1/2)x+1/2 by rearranging

y=mx+c compare them

m= 1/2

y+4=(-1/2)(x+2)

y=(-1/2)x-5 by rearraging

y=mx+c

slop(m)=-1/2

So we coclude from two equations their slop are not equal so we can says they are not parallal...

Answer 2

Put each equation in the form y = mx + b. Slope = m.

2y - x = 1

2y = x + 1

y = (1/2)x +(1/2) Slope = 1/2

y + 4 = (-1/2)(x + 2)

y + 4 = (-1/2)x - 1

y = (-1/2)x - 5 Slope = -1/2

The lines are not parallel since the slopes are not the same. The lines are not perpendicular since the product of the slopes is not -1. (In other words slope of second line ≠ -1 / (slope of first line))