Step-by-step explanation:
Hey there!
Here,
The equations are;
2x+3y = 4
2x+3y-4=0..........(i).
2y = 3x + 17
3x -2y +17 =0.......(ii).
Now,
From equation (i).
[tex]slope(m1) = \frac{ - coeff. \: of \: x}{ \: coeff. \: of \: y} [/tex]
Put values.
[tex]m1 = \frac{ - 2}{3} [/tex]
Therefore the slope is-2/3.
From equation (ii).
[tex]slope(m2) = \frac{ - coeff. \: of \: x}{ \: coeff. \: of \: y} [/tex]
Put value.
[tex]m2 = \frac{ - 3}{ - 2} [/tex]
Therefore the slope is 3/2.
For, parallel lines;
m1= m2
-2/3 is not equal to 3/2.
So, they are not parallel lines.
For, perpendicular lines;
m1 × m2 = -1
[tex] \frac{ - 2}{3} \times \frac{3}{2} [/tex]
After simplifying it we get, (-1).
Therefore they are perpendicular to eachother.
Hope it helps...
