Question

Find the distance between the lines 3
x+ 4y= 9 and 6x+ 8y= 15.

Answer 1

3x+ 4y= 9
6x+ 8y= 15

y = -3/4x + 9/4
y = -6/8x + 15/8

y = -3/4x + 9/4
y = -3/4x + 15/8

parallel lines.

Answer 2

Thank you Sir

Answer 3

yea, now since we know the lines are parallel, we can just find the distance between where they hit the y axis.

Answer 4

distance between the lines = 9/4-15/8

Answer 5

That's not the distance between the lines. For that we need a perpendicular line to both of them. 4/3 x works. Now we solve this system to see where the intersections are and find the pythagorean distance between them.:
\[y=-3x/4+15/8=4x/3 ...x=0.9, y=1.2\]
\[y=-3x/4+9/4=4x/3 ...x=1.08, y=1.44\]
\[distance=\sqrt{.18^2+.24^2}=.3 \neq9/4-15/8=.375\]