Question

What is the equation of the line perpendicular to `y=5/16x` that passes through `(-5,4)`?

Answer 1

`y=-16/5x-12`

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=5/16x" is in this form"`

`"with slope "=5/16" and y-intercept "=0`

`"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/(5/16)=-16/5`

`rArry=-16/5x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute "(-5,4)" into the partial equation"`

`4=16+brArrb=4-16=-12`

`rArry=-16/5x-12larrcolor(red)"equation of perpendicular"`