Answer:
They are perpendicular
Step-by-step explanation:
To solve this problem .
we will convert the equations in slope intercept form.
Slope intercept form of equation is y = mx+c
where m is slope of line and c is y intercept.
________________________________
equation 1 is
2x+y = 4
=> y =4 - 2x or y = -2x + 4
comparing it with y = mx + c
m = -2 , c = 4
_________________________________________
equation 2 is y = one halfx + 4 ( one half is same as 1/2)
so equation is
y = x/2 +4
comparing it with y = mx + c
m = 1/2 , c = 4
_________________________________________
Now lets evaluate options
They are parallel. wrong option
For lines to be parallel slope should be same.
But here slope are different -2 and 1/2 .
Thus lines are not parallel.
__________________________________________
They are perpendicular. correct option
For lines to be perpendicular, product of slope should be equal to -1.
-2*1/2 = -1
we can see that product of slope should be equal to -1 .
Thus lines are perpendicular
______________________________________
They are the same line. wrong option
For lines to be same both slope and y intercept should be same.
Y intercept is same but the slopes are different -2 and 1/2 .
Thus lines are not the same line.
__________________________________________
They are not related. wrong option
As we have found that the lines are perpendicular .
So this option is intuitively wrong
