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.
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equation 1 is
2x+y = 4
=> y =4 - 2x or y = -2x + 4
comparing it with y = mx + c
m = -2 , c = 4
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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
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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.
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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
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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.
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They are not related. wrong option
As we have found that the lines are perpendicular .
So this option is intuitively wrong
![\sqrt[3]{x}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7Bx%7D%20)
for specific values of x. Basically, we are taking the cube roots of these numbers.![r(-2.197) = \sqrt[3]{-2.197} = -1.3\\\\ r(-1.331) = \sqrt[3]{-1.331} = -1.1\\\\ r(0) = \sqrt[3]{0} = 0 \\\\ r(1.331) = \sqrt[3]{1.331} = 1.1\\\\r(2.197) = \sqrt[3]{2.197} = 1.3\\\\r(-3.375) = \sqrt[3]{-3.375} = 1.5\\\\r(4.913) = \sqrt[3]{4.913} = 1.7\\\\](https://tex.z-dn.net/?f=r%28-2.197%29%20%3D%20%5Csqrt%5B3%5D%7B-2.197%7D%20%3D%20-1.3%5C%5C%5C%5C%20r%28-1.331%29%20%3D%20%5Csqrt%5B3%5D%7B-1.331%7D%20%3D%20-1.1%5C%5C%5C%5C%20r%280%29%20%3D%20%5Csqrt%5B3%5D%7B0%7D%20%3D%200%20%5C%5C%5C%5C%20r%281.331%29%20%3D%20%5Csqrt%5B3%5D%7B1.331%7D%20%3D%201.1%5C%5C%5C%5Cr%282.197%29%20%3D%20%5Csqrt%5B3%5D%7B2.197%7D%20%3D%201.3%5C%5C%5C%5Cr%28-3.375%29%20%3D%20%5Csqrt%5B3%5D%7B-3.375%7D%20%3D%201.5%5C%5C%5C%5Cr%284.913%29%20%3D%20%5Csqrt%5B3%5D%7B4.913%7D%20%3D%201.7%5C%5C%5C%5C)
