Answer:
Perpendicular
Step-by-step explanation:
General equation of line: [tex]y=mx+c[/tex]
Line 1: 6x+10y=20
Convert in general equation
[tex]10y = 20-6x[/tex]
[tex]y = \frac{20-6x}{10}[/tex]
[tex]y =2-\frac{6}{10}x[/tex]
[tex]y =2-\frac{3}{5}x[/tex]
Line 2: 5x-3y=21
Convert in general equation
[tex]5x-21=3y[/tex]
[tex]\frac{5x-21}{3}=3y[/tex]
[tex]\frac{5}{3}x-7=3y[/tex]
if slopes are equal then the lines are parallel
If the product of slopes is -1 then they are perpendicular
Since[tex]\frac{-3}{5} \neq \frac{5}{3}[/tex]
So, lines are not parallel
[tex]\frac{-3}{5} \times \frac{5}{3}[/tex]
[tex]-1[/tex]
Since the product of slopes is -1
Hence the given lines are perpendicular
