How do you find slope of the line perpendicular to the line 5x+2y=10?

2 Answers
Apr 19, 2018

Answer:

#"perpendicular slope "=2/5#

Explanation:

#"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"#

#"rearrange "5x+2y=10" into this form"#

#"subtract 5x from both sides and divide all terms by 2"#

#2y=-5x+10#

#rArry=-5/2x+5larrcolor(blue)"in slope-intercept form"#

#"with slope "=-5/2#

#"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/(-5/2)=2/5#

Apr 19, 2018

The way we find the equations for a family of perpendicular lines is to swap the coefficients on #x# and #y# and negate one of them: #2x - 5y = text{constant}# or #y = 2/5 x + text{constant} #, a slope of #2/5#.