Question

How do you write an equation of a line passing through (4, -3), perpendicular to `y=-4x+3`?

Answer 1

`y=1/4x-4`

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=-4x+3" is in this form"`

`"with slope m "=-4`

`"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/(-4)=1/4`

`rArry=1/4x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute "(4,-3)" into the partial equation"`

`-3=1+brArrb=-3-1=-4`

`rArry=1/4x-4larrcolor(red)"perpendicular line"`