A) \[y=2x+6\]
B) \[y=2x-6\]
C) \[y=2x+3\]
D) \[y=2x+4\]
Correct Answer: A
Solution :
Here, it is given that lines \[{{l}_{1}}\] and \[{{l}_{2}}\] are parallel. We know that, the parallel line on the co-ordinate planes have the same slope. i.e. line \[{{l}_{1}}\] must have the same slope as line \[{{l}_{2}}\] Equation of line \[{{l}_{1}}\] is \[y=2x-4.\] Compare if with \[y=mx+c\] from, Slope = co-efficient of x term = 2. So, line have slope = 2. Now, line \[{{l}_{1}}\] have the equation of form, \[y=2x+c.\] For finding the value of c which is a y-inter-cept of line; put \[x=0\]and \[y=6,\]as line crosses the y-axis at point \[(0,6)\]. \[\therefore \] \[y=2x+c\] or \[6=2(0)+c\] or \[c=6\]. So, the equation of line \[{{l}_{1}}\] is \[y=2x+6.\]
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