Step-by-step explanation:
Hey there!
Here, The equations are;
-3y=5x+6
5x+3y+6=0.........(i)
10x-6y+4 =0......(ii)
y= -3/5x+3.......(iii)
From equation (i).
[tex]slope(m1) = \frac{ - coeff. \: ofx}{coeff. \: of \: y} [/tex]
Put all values.
[tex]m1 = \frac{ - 5}{3} [/tex]
Now, from equation (ii).
[tex]m2 = \frac{ - coeff. \: of \: x}{coeff. \: of \: y} [/tex]
Put all values.
[tex]m2 = \frac{ - 10 }{ - 6} [/tex]
[tex]m2 = \frac{5}{3} [/tex]
As m1 is not equal to m2 it is not parallel lines.
For perpendicular lines;
m1×m2= -1.
[tex] \frac{ - 5}{3} \times \frac{5}{3} [/tex]
After simplifying it we get -25/9 which is not equal to-1. So, it is not perpendicular lines.
Therefore, the lines are neither parallel nor perpendicular.
But the lines of equation (ii) and (iii) are perpendicular to eachother.
-3/5×5/3= -1
[ so, the line (ii) and (iii) are perpendicular to eachother but others are neither]
Hope it helps...
