Option B is the correct answer
In order to find whether or not a line is parallel to another line, both lines must have the same slope.
Given the slope_intercept form of the line equation as:
[tex]\begin{gathered} y=mx+c \\ m=\text{slope} \end{gathered}[/tex]
m must be equal for both lines.
Now let us proceed to analyse each option.
Option 1:
[tex]\begin{gathered} \text{ Line 1:} \\ y=-2 \\ \text{ Line 2:} \\ y=4 \\ \text{ } \\ \text{ In both lines, m = 0} \end{gathered}[/tex]
Therefore, the lines are parallel.
Option 2:
[tex]\begin{gathered} \text{ Line 1:} \\ x+y=3\text{ (re-write in slope intercpet form)} \\ y=-x+3 \\ \text{slope(m) = -1} \\ \\ \text{ LIne 2:} \\ x-y=3\text{ (re-write in slope intercept form)} \\ y=x+3 \\ \text{slope(m) = 1} \end{gathered}[/tex]
