To determine whether the lines are parallel or perpendicular, we can compare their slopes. The given equations are:
(a)2y+x=-12
(b)2y=3x-8
Let's rewrite each equation in the slope-intercept form (y=mx+b), where
m is the slope:
(a) 2y+x=−12 can be rewritten as 2y=−x−12, and then dividing both sides by 2, we get y=−0.5x−6. So, the slope of line (a) is −0.5.
(b) 2y=3x-8 can be rewritten as y=1.5x-4.
So, the slope of line (b) is 1.5
Now, we can compare the slopes:
- If the slopes are equal, the lines are parallel.
- If the slopes are negative reciprocals (the product of the slopes is -1), the lines are perpendicular.
In this case, the slopes are not equal, and the product of
slopes = (-0.5) x 1.5 = -0.75
Therefore, the lines (a) and (b) are neither parallel nor perpendicular.