Question

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

Answer 1

`y=-3/5x-23/5`

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"`