Question

What is the equation of the line perpendicular to `y=15/4x` that passes through `(-2,7)`?

Answer 1

`y=-4/15x+97/15`

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=15/4x" is in this form"`

`"with "m=15/4" and "b=0`

`"given the equation of 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/(15/4)=-4/15`

`y=-4/15x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute "(-2,7)" into the partial equation"`

`7=8/15+brArrb=105/15-8/15=97/15`

`y=-4/15x+97/15larrcolor(red)"equation of perpendicular line"`