Tell whether the lines in each pair are parallel, perlendicular, or neither.

Question

ax - by = 5; -ax + by = 2

 

Also this one

 

ax + by = 8; bx - ay = 1

 

I do not understand. Please help.

Answer 1

ax-by=5

-ax+by=2

write them in the slope-intercept form

ax-by=5

-by=-ax+5

y=(-ax/-b)+(5/-b)

y=(a/b)x+(5/-b), where the slope is a/b

-ax+by=2

by=ax+2

y=(a/b)x+(2/b), where the slope is a/b

the lines are parallel because they have the same slope

 

ax+by=8

bx-ay=1

write them in slope-intercept form

by=-ax+8

y=(-a/b)x+(8/b), where the slope is (-a/b)

bx-ay=1

-ay=-bx+1

y=(-b/-a)x+(1/-a)

y=(b/a)x+(1/-a), where the slope is b/a

the lines are perpendicular to each other because the slopes are negative reciprocals of each other