Question

What is the equation of the line perpendicular to `y=-11/16x` that passes through `(3,7)`?

Answer 1

`16x-11y=-29`

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=-11/16x" is in this form with "m=-11/16,b=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/(-11/16)=16/11`

`rArry=16/11+blarrcolor(blue)"is the partial equation"`

`"to find b substitute "(3,7)" into the partial equation"`

`7=48/11+brArrb=77/11-48/11=29/11`

`rArry=16/11x+29/11larrcolor(red)"in slope-intercept form"`

`"multiply all terms by 11 and rearrange"`

`11y=16x+29`

`rArr16x-11y=-29larrcolor(red)"in standard form"`