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

3 Answers
Jun 7, 2018

Answer:

#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#

Jun 7, 2018

Answer:

#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#

Jun 7, 2018

Answer:

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#