Question

How do you write an equation of a line passing through (2, -2), perpendicular to `y = –x + 3`?

Answer 1

`y=x-4`

Explanation:

`"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`

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

`"with "m=-1`

`rArrm_(color(red)"perpendicular")=-1/(-1)=1`

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

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

`-2=2+brArrb=-4`

`rArry=x-4larrcolor(red)"in slope-intercept form"`