Step-by-step explanation:
Hey, there!
Let's check whether the lines are parallel, perpendicular or neither.
Fistly let's check of parallel ,
Let me tell you when two st. lines are paralle, then their slope are equal.
Given equation are,
3x - 4y = 9.........(i)
8x+y = 12 ..........(ii)
Now,
From equation (i)
[tex]slope \: (m1) = \frac{ - coffe. \: ofx}{coffe. \: of \: y} [/tex]
[tex]\: slope \: (m1) = \frac{ - 3}{ - 4} [/tex]
[tex]therefore \: slope \: (m1) = \frac{3}{4} [/tex]
now, again slope from equation (ii).
[tex]slope(m2) = \frac{ - coffe.of \: x}{coffe. \: of \: y} [/tex]
[tex]slope \: (m2) = \frac{ - 8}{1} [/tex]
Therefore, the slope of equation (ii) is -8.
Since, Their slopes are not equal, they are not parallel.
Now, let's check for perpendicular,
To be perpendicular, slope (m1)× slope (m2)= -1
now,
[tex] = \frac{3}{4} \times - 8 [/tex]
= 3×-2
= -6.
So, the equations are neither parallel nor perpendicular.
Hope it helps...
