Question

Find the slope of the line that is parallel and perpendicular to the given line.

y = 1/3x + 5

m ll =
⊥ =

Answer 1

`(1)/(3)` and - 3

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y =
`(1)/(3)` x + 5 ← is in slope- intercept form

with slope m =
`(1)/(3)`

Parallel lines have equal slopes, thus

`m_(parallel)` =
`(1)/(3)`

Give a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((1)/(3) )` = - 3

Answer 2

|| slope= 1/3

⊥ slope=-3

Explanation:

The line is y=1/3x+5

Parallel slopes are the same (think about parallel lines and how they will never intersect- that means that slopes of those lines will never intersect so they have to be the same)

That means that the || slope will be 1/3.

Perpendicular slopes are negative and reciprocal (if you multiply them, they will equal -1)

Which means to solve for the slope perpendicular, use this equation

1/3m=-1

multiply by 3 on both sides

m=-3

So that means the ⊥ slope will be -3.

hope this helps!