# How do you find the equation of line through point (-6, -1) perpendicular to line #5x-3y=2#?

##### 1 Answer

Dec 20, 2017

#### Explanation:

#"given the slope m of a line then the slope of a line"#

#"perpendicular to it is"#

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

#"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-3y=2" into this form"#

#rArry=5/3x-2/3larr" with "m=5/3#

#rArrm_(color(red)"perpendicular")=-1/(5/3)=-3/5#

#rArry=-3/5x+blarrcolor(blue)"is the partial equation"#

#"to find b substitute "(-6,-1)#

#"into the partial equation"#

#-1=18/5+brArrb=-23/5#

#rArry=-3/5x-23/5larrcolor(red)"in slope-intercept form"#