Question

What is the equation of the line perpendicular to `y=7/16x` that passes through `(6,-5)`?

Answer 1

`y=-16/7x+61/7`

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=7/16x" is in this form"`

`"with slope m "=7/16`

`"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/(7/16)=-16/7`

`rArry+5=-16/7(x-6)larrcolor(blue)"point-slope form"`

`rArry+5=-16/7x+96/7`

`rArry=-16/7x+61/7larrcolor(blue)"slope-intercept form"`