Question

How do you write an equation of a line passing through (-16, -11), perpendicular to `y = -4x -2`?

Answer 1

`y=1/4x-7`

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"`

`y=-4x-2" is in this form"`

`"with "m=-4`

`"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/(-4)=1/4`

`rArry=1/4x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute "(-16,-11)" into the partial equation"`

`-11=-4+brArrb=-11+4=-7`

`rArry=1/4x-7larrcolor(red)"perpendicular equation"`