Question

What is the equation of the line perpendicular to `y=-15/4x` that passes through `(-1,7)`?

Answer 1

`y=4/15x+109/15`

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 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`

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

`"to find b substitute "(-1,7)" into the partial equation"`

`7=-4/15+brArrb=105/15+4/15=109/15`

`rArry=4/15x+109/15larrcolor(red)"perpendicular equation"`