Question

How do you find the slope of the line parallel to and perpendicular to `y+3=3x+2`?

Answer 1

`m'=3`

`m' = -1/3`

Explanation:

`y+3=3x+2`

convert to slope intercept form `y=mx+b`

`y=3x-1`

So slope of this line `m=3`

Slope of a parallel line: `m'=m`:

`m'=3`

Slope of a perpendicular line `m' = -1/m`

`m' = -1/3`

Answer 2

`3" and "-1/3`

Explanation:

`• " parallel lines have equal slopes"`

`"the equation of a line in "color(blue)"slope-intercept form"` is.

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

`y+3=3x+2" can be written as"`

`y=3x-1larrcolor(blue)"in slope-intercept form"`

`"with slope m "=3" and y-intercept "=-1`

`"thus a line parallel to it has slope "=3`

`"given a line with slope m then the slope of a line"`
`"perpendicular to it is"`

`•color(white)(x)m_(color(red)"perpendicular")=-1/m`

`rArrm_("perpendicular")=-1/3`

`"thus a line perpendicular to it has slope "=-1/3`

Answer 3

Parallel slope: `3`
Perpendicular slope: `-1/3`

Explanation:

I'm assuming that you're actually asking two questions, so let's split them up: in general, given two lines with slopes `m_1` and `m_2`, the lines are parallel if `m_1 = m_2`, while their are perpendicular if `m_1 = - 1/m_2`

To find the slope of a line from its equation, you can write it in the form `y=mx+b`. The slope will be the `x` coefficient, i.e. `m`.

In your case, you only need to subtract `3` from both sides to get

`y = 3x-1`

so the slope is `3`.

This means that any line parallel to the given line will have slope `3` as well, while all the perpendicular lines will have slope `-1/3`