To find out if two lines are parallel or perpendicular, we need to examine their slopes.
The equation of a line is typically written in the form y = mx + b, where 'm' stands for the slope of the line.
The given lines are:
1. y+(1)/(2)x=7. To write it in the form y = mx + b, we rewrite it as y = -0.5x + 7. Therefore, the slope (m1) of this line is -0.5.
2. The second line is already in the form y = mx, y=2x. Therefore, the slope (m2) of this line is 2.
Having identified the slopes of the two lines, we can now check whether the lines are parallel or perpendicular.
Two lines are parallel if their slopes are equal. In our case, m1 is not equal to m2 (-0.5 ≠ 2), so the lines are not parallel.
Two lines are perpendicular if the product of their slopes is -1. In our cases, when we multiply m1 and m2, we have -0.5*2 which equals -1. Therefore, the lines are perpendicular.
In conclusion, the given lines are not parallel but are perpendicular to each other.